id
large_string | title
large_string | abstract
large_string | publish_date
date32 | update_date
date32 | categories
large list | authors
large_string |
|---|---|---|---|---|---|---|
hep-th/9109015
|
On the solutions to the string equation
|
The set of solutions to the string equation $[P,Q]=1$ where $P$ and $Q$ are
differential operators is described.It is shown that there exists one-to-one
correspondence between this set and the set of pairs of commuting differential
operators.This fact permits us to describe the set of solutions to the string
equation in terms of moduli spa- ces of algebraic curves,however the direct
description is much simpler. Some results are obtained for the superanalog to
the string equation where $P$ and $Q$ are considered as superdifferential
operators. It is proved that this equation is invariant with respect to
Manin-Radul, Mulase-Rabin and Kac-van de Leur KP-hierarchies.
| 1991-09-10
| 2009-10-22
|
[
"hep-th"
] |
A.Schwarz
|
hep-th/9109014
|
Generalized Drinfeld-Sokolov Hierarchies II: The Hamiltonian Structures
|
In this paper we examine the bi-Hamiltonian structure of the generalized
KdV-hierarchies. We verify that both Hamiltonian structures take the form of
Kirillov brackets on the Kac-Moody algebra, and that they define a coordinated
system. Classical extended conformal algebras are obtained from the second
Poisson bracket. In particular, we construct the $W_n^l$ algebras, first
discussed for the case $n=3$ and $l=2$ by A. Polyakov and M. Bershadsky.
| 1991-09-10
| 2015-06-26
|
[
"hep-th"
] |
Nigel J. Burroughs, Mark F. deGroot, Timothy J. Hollowood and J. Luis
Miramontes
|
hep-th/9109010
|
W3 Constructions on Affine Lie Algebras
|
We use an argument of Romans showing that every Virasoro construction leads
to realizations of $W_3$, to construct $W_3$ realizations on arbitrary affine
Lie algebras. Solutions are presented for generic values of the level as well
as for specific values of the level but with arbitrary parameters. We give a
detailed discussion of the $\aff{su}(2)_\ell$-case. Finally, we discuss
possible applications of these realizations to the construction of $W$-strings.
| 1991-09-09
| 2009-10-22
|
[
"hep-th"
] |
A. Deckmyn and S. Schrans
|
hep-th/9109009
|
Bi-Hamiltonian Sturcture of Super KP Hierarchy
|
We obtain the bi-Hamiltonian structure of the super KP hierarchy based on the
even super KP operator $\Lambda = \theta^{2} + \sum^{\infty}_{i=-2}U_{i}
\theta^{-i-1}$, as a supersymmetric extension of the ordinary KP bi-Hamiltonian
structure. It is expected to give rise to a universal super $W$-algebra
incorporating all known extended superconformal $W_{N}$ algebras by reduction.
We also construct the super BKP hierarchy by imposing a set of anti-self-dual
constraints on the super KP hierarchy.
| 1991-09-06
| 2007-05-23
|
[
"hep-th"
] |
Feng Yu
|
hep-th/9109008
|
Effective Superstrings
|
We generalize the method of quantizing effective strings proposed by
Polchinski and Strominger to superstrings. The Ramond-Neveu-Schwarz string is
different from the Green-Schwarz string in non-critical dimensions. Both are
anomaly-free and Poincare invariant. Some implications of the results are
discussed. The formal analogy with 4D (super)gravity is pointed out.
| 1991-09-05
| 2009-10-22
|
[
"hep-th"
] |
Zhu Yang
|
hep-th/9109007
|
High Temperature Limit of the Confining Phase
|
The deconfining transition in non-Abelian gauge theory is known to occur by a
condensation of Wilson lines. By expanding around an appropriate Wilson line
background, it is possible at large $N$ to analytically continue the confining
phase to arbitrarily high temperatures, reaching a weak coupling confinement
regime. This is used to study the high temperature partition function of an
$SU(N)$ electric flux tube. It is found that the partition function corresponds
to that of a string theory with a number of world-sheet fields that diverges at
short distance.
| 1991-09-05
| 2009-10-09
|
[
"hep-th"
] |
Joseph Polchinski
|
hep-th/9109006
|
(2+1)-Dimensional Chern-Simons Gravity as a Dirac Square Root
|
For (2+1)-dimensional spacetimes with the spatial topology of a torus, the
transformation between the Chern-Simons and ADM versions of quantum gravity is
constructed explicitly, and the wave functions are compared. It is shown that
Chern-Simons wave functions correspond to modular forms of weight 1/2, that is,
spinors on the ADM moduli space, and that their evolution (in York's
``extrinsic time'' variable) is described by a Dirac equation. (This version
replaces paper 9109006, which was garbled by my mailer.)
| 1991-09-04
| 2014-11-18
|
[
"hep-th"
] |
Steven Carlip
|
hep-th/9109004
|
Bosonisation of the Complex-boson realisation of $W_\infty$
|
We bosonise the complex-boson realisations of the $W_\infty$ and
$W_{1+\infty}$ algebras. We obtain nonlinear realisations of $W_\infty$ and
$W_{1+\infty}$ in terms of a pair of fermions and a real scalar. By further
bosonising the fermions, we then obtain realisations of $W_\infty$ in terms of
two scalars. Keeping the most non-linear terms in the scalars only, we arrive
at two-scalar realisations of classical $w_\infty$.
| 1991-09-04
| 2009-10-22
|
[
"hep-th"
] |
X. Shen and X.J. Wang
|
hep-th/9109005
|
World Sheet and Space Time Physics in Two Dimensional (Super) String
Theory
|
We show that tree level ``resonant'' $N$ tachyon scattering amplitudes, which
define a sensible ``bulk'' S -- matrix in critical (super) string theory in any
dimension, have a simple structure in two dimensional space time, due to
partial decoupling of a certain infinite set of discrete states. We also argue
that the general (non resonant) amplitudes are determined by the resonant ones,
and calculate them explicitly, finding an interesting analytic structure.
Finally, we discuss the space time interpretation of our results.
| 1991-09-04
| 2009-10-22
|
[
"hep-th"
] |
P. Di Francesco and D. Kutasov
|
hep-th/9109002
|
Ashtekar's Approach to Quantum Gravity
|
A review is given of work by Abhay Ashtekar and his colleagues Carlo Rovelli,
Lee Smolin, and others, which is directed at constructing a nonperturbative
quantum theory of general relativity.
| 1991-09-03
| 2007-05-23
|
[
"hep-th"
] |
Gary T. Horowitz
|
hep-th/9109003
|
The renormalization group flow in 2D N=2 SUSY Landau-Ginsburg models
|
We investigate the renormalization of N=2 SUSY L-G models with central charge
$c=3p/(2+p)$ perturbed by an almost marginal chiral operator. We calculate the
renormalization of the chiral fields up to $gg{^*}$ order and of nonchiral
fields up to $g(g^{*})$ order. We propose a formulation of the
nonrenormalization theorem and show that it holds in the lowest nontrivial
order. It turns out that, in this approximation, the chiral fields can not get
renormalized $\Phi^{k}=\Phi^{k}_{0}$. The $\beta$ function then remains
unchanged $\beta=\epsilon gr$.
| 1991-09-03
| 2008-11-26
|
[
"hep-th"
] |
Jadwiga Bienkowska
|
hep-th/9109001
|
Fractional Superstrings with Space-Time Critical Dimensions Four and Six
|
We propose possible new string theories based on local world-sheet symmetries
corresponding to extensions of the Virasoro algebra by fractional spin
currents. They have critical central charges $c=6(K+8)/(K+2)$ and Minkowski
space-time dimensions $D=2+16/K$ for $K\geq2$ an integer. We present evidence
for their existence by constructing modular invariant partition functions and
the massless particle spectra. The dimension $4$ and $6$ strings have
space-time supersymmetry.
| 1991-09-02
| 2009-10-22
|
[
"hep-th"
] |
Philip C. Argyres and S.-H. Henry Tye
|
hep-th/9108027
|
Factorization and Topological States in $c=1$ Matter Coupled to 2-D
Gravity
|
Factorization of the $N$-point amplitudes in two-dimensional $c=1$ quantum
gravity is understood in terms of short-distance singularities arising from the
operator product expansion of vertex operators after the Liouville zero mode
integration. Apart from the tachyon states, there are infinitely many
topological states contributing to the intermediate states.
| 1991-08-30
| 2009-10-22
|
[
"hep-th"
] |
Norisuke Sakai, Yoshiaki Tanii
|
hep-th/9108026
|
Superstring in Two Dimensional Black Hole
|
We construct superstring theory in two dimensional black hole background
based on supersymmetric $SU(1,1)/U(1)$ gauged Wess-Zumino-Witten model.
| 1991-08-29
| 2011-04-20
|
[
"hep-th"
] |
Shin'ichi Nojiri
|
hep-th/9108024
|
On the S-matrix of the Sub-leading Magnetic Deformation of the
Tricritical Ising Model in Two Dimensions
|
We compute the $S$-matrix of the Tricritical Ising Model perturbed by the
subleading magnetic operator using Smirnov's RSOS reduction of the
Izergin-Korepin model. The massive model contains kink excitations which
interpolate between two degenerate asymmetric vacua. As a consequence of the
different structure of the two vacua, the crossing symmetry is implemented in a
non-trivial way. We use finite-size techniques to compare our results with the
numerical data obtained by the Truncated Conformal Space Approach and find good
agreement.
| 1991-08-27
| 2015-06-26
|
[
"hep-th"
] |
F. Colomo, A. Koubek, G. Mussardo
|
hep-th/9108023
|
Fock space resolutions of the Virasoro highest weight modules with c<=1
|
We extend Felder's construction of Fock space resolutions for the Virasoro
minimal models to all irreducible modules with $c\leq 1$. In particular, we
provide resolutions for the representations corresponding to the boundary and
exterior of the Kac table.
| 1991-08-27
| 2009-09-11
|
[
"hep-th"
] |
Peter Bouwknegt, Jim McCarthy and Krzysztof Pilch
|
hep-th/9108019
|
String Theory in Two Dimensions
|
I review some of the recent progress in two-dimensional string theory, which
is formulated as a sum over surfaces embedded in one dimension.
| 1991-08-26
| 2008-02-03
|
[
"hep-th"
] |
Igor R. Klebanov
|
hep-th/9108021
|
The big picture
|
We discuss the conformal field theory and string field theory of the NSR
superstring using a BRST operator with a nonminimal term, which allows all
bosonic ghost modes to be paired into creation and annihilation operators.
Vertex operators for the Neveu-Schwarz and Ramond sectors have the same ghost
number, as do string fields. The kinetic and interaction terms are the same for
Neveu-Schwarz as for Ramond string fields, so spacetime supersymmetry is closer
to being manifest. The kinetic terms and supersymmetry don't mix levels,
simplifying component analysis and gauge fixing.
| 1991-08-26
| 2009-10-22
|
[
"hep-th"
] |
N. Berkovits, M.T. Hatsuda, and W. Siegel
|
hep-th/9108020
|
String Theory and the Donaldson Polynomial
|
It is shown that the scattering of spacetime axions with fivebrane solitons
of heterotic string theory at zero momentum is proportional to the Donaldson
polynomial.
| 1991-08-26
| 2009-09-17
|
[
"hep-th"
] |
J.A.Harvey and A.Strominger
|
hep-th/9108022
|
Superstring Compactification and Target Space Duality
|
This review talk focusses on some of the interesting developments in the area
of superstring compactification that have occurred in the last couple of years.
These include the discovery that ``mirror symmetric" pairs of Calabi--Yau
spaces, with completely distinct geometries and topologies, correspond to a
single (2,2) conformal field theory. Also, the concept of target-space duality,
originally discovered for toroidal compactification, is being extended to
Calabi--Yau spaces. It also associates sets of geometrically distinct manifolds
to a single conformal field theory.
A couple of other topics are presented very briefly. One concerns conceptual
challenges in reconciling gravity and quantum mechanics. It is suggested that
certain ``distasteful allegations" associated with quantum gravity such as loss
of quantum coherence, unpredictability of fundamental parameters of particle
physics, and paradoxical features of black holes are likely to be circumvented
by string theory. Finally there is a brief discussion of the importance of
supersymmetry at the TeV scale, both from a practical point of view and as a
potentially significant prediction of string theory.
| 1991-08-26
| 2007-05-23
|
[
"hep-th"
] |
John H. Schwarz
|
hep-th/9108025
|
Correlation functions in super Liouville theory
|
We calculate three- and four-point functions in super Liouville theory
coupled to super Coulomb gas on world sheets with spherical topology. We first
integrate over the zero mode and assume that a parameter takes an integer
value. After calculating the amplitudes, we formally continue the parameter to
an arbitrary real number. Remarkably the result is completely parallel to the
bosonic case, the amplitudes being of the same form as those of the bosonic
case.
| 1991-08-24
| 2009-10-22
|
[
"hep-th"
] |
E. Abdalla, M.C.B. Abdalla, D.Dalmazi, Koji Harada
|
hep-th/9108015
|
A $U(N)$ Gauge Theory in Three Dimensions as an Ensemble of Surfaces
|
A particular $U(N)$ gauge theory defined on the three dimensional
dodecahedral lattice is shown to correspond to a model of oriented
self-avoiding surfaces. Using large $N$ reduction it is argued that the model
is partially soluble in the planar limit.
| 1991-08-23
| 2009-10-22
|
[
"hep-th"
] |
F. David, H. Neuberger
|
hep-th/9108018
|
Real Forms of Complex Quantum Anti de Sitter Algebra $U_q (Sp(4,C))$ and
their Contraction Schemes
|
We describe four types of inner involutions of the Cartan-Weyl basis
providing (for $ |q|=1$ and $q$ real) three types of real quantum Lie algebras:
$U_{q}(O(3,2))$ (quantum D=4 anti-de-Sitter), $U_{q}(O(4,1))$ (quantum D=4
de-Sitter) and $U_{q}(O(5))$. We give also two types of inner involutions of
the Cartan-Chevalley basis of $U_{q}(Sp(4;C))$ which can not be extended to
inner involutions of the Cartan-Weyl basis. We outline twelve contraction
schemes for quantum D=4 anti-de-Sitter algebra. All these contractions provide
four commuting translation generators, but only two (one for $ |q|=1$, second
for $q$ real) lead to the quantum \po algebra with an undeformed space
rotations O(3) subalgebra.
| 1991-08-23
| 2009-10-22
|
[
"hep-th"
] |
J. Lukierski, A. Novicki and H. Ruegg
|
hep-th/9108017
|
A New Solution to the Star--Triangle Equation Based on U$_q$(sl(2)) at
Roots of Unit
|
We find new solutions to the Yang--Baxter equation in terms of the
intertwiner matrix for semi-cyclic representations of the quantum group
$U_q(s\ell(2))$ with $q= e^{2\pi i/N}$. These intertwiners serve to define the
Boltzmann weights of a lattice model, which shares some similarities with the
chiral Potts model. An alternative interpretation of these Boltzmann weights is
as scattering matrices of solitonic structures whose kinematics is entirely
governed by the quantum group. Finally, we consider the limit $N\to\infty$
where we find an infinite--dimensional representation of the braid group, which
may give rise to an invariant of knots and links.
| 1991-08-23
| 2009-10-22
|
[
"hep-th"
] |
Cesar Gomez and German Sierra
|
hep-th/9108016
|
Non-Perturbative 2D Quantum Gravity, Again
|
This is a talk given by S.D. at the the workshop on Random Surfaces and 2D
Quantum Gravity, Barcelona 10-14 June 1991. It is an updated review of recent
work done by the authors on a proposal for non-perturbatively stable 2D quantum
gravity coupled to c<1 matter, based on the flows of the (generalised) KdV
hierarchy.
| 1991-08-23
| 2009-10-22
|
[
"hep-th"
] |
S.Dalley, C.Johnson and T.Morris
|
hep-th/9108014
|
Loop Equations and the Topological Phase of Multi-Cut Matrix Models
|
We study the double scaling limit of mKdV type, realized in the two-cut
Hermitian matrix model. Building on the work of Periwal and Shevitz and of
Nappi, we find an exact solution including all odd scaling operators, in terms
of a hierarchy of flows of $2\times 2$ matrices. We derive from it loop
equations which can be expressed as Virasoro constraints on the partition
function. We discover a ``pure topological" phase of the theory in which all
correlation functions are determined by recursion relations. We also examine
macroscopic loop amplitudes, which suggest a relation to 2D gravity coupled to
dense polymers.
| 1991-08-22
| 2015-06-26
|
[
"hep-th"
] |
C. Crnkovic, M. Douglas, G. Moore
|
hep-th/9108012
|
On the Perturbations of String-Theoretic Black Holes
|
The perturbations of string-theoretic black holes are analyzed by
generalizing the method of Chandrasekhar. Attention is focussed on the case of
the recently considered charged string-theoretic black hole solutions as a
representative example. It is shown that string-intrinsic effects greatly alter
the perturbed motions of the string-theoretic black holes as compared to the
perturbed motions of black hole solutions of the field equations of general
relativity, the consequences of which bear on the questions of the scattering
behavior and the stability of string-theoretic black holes. The explicit forms
of the axial potential barriers surrounding the string-theoretic black hole are
derived. It is demonstrated that one of these, for sufficiently negative values
of the asymptotic value of the dilaton field, will inevitably become negative
in turn, in marked contrast to the potentials surrounding the static black
holes of general relativity. Such potentials may in principle be used in some
cases to obtain approximate constraints on the value of the string coupling
constant. The application of the perturbation analysis to the case of
two-dimensional string-theoretic black holes is discussed.
| 1991-08-22
| 2007-05-23
|
[
"hep-th"
] |
Gerald Gilbert
|
hep-th/9108013
|
Differential Equations for Periods and Flat Coordinates in Two
Dimensionsional Topological Matter Theories
|
We derive directly from the N=2 LG superpotential the differential equations
that determine the flat coordinates of arbitrary topological CFT's.
| 1991-08-22
| 2009-10-22
|
[
"hep-th"
] |
W.Lerche, D.Smit, and N. Warner
|
hep-th/9108010
|
String Winding in a Black Hole Geometry
|
$U(1)$ zero modes in the $SL(2,R)_k/U(1)$ and $SU(2)_k/U(1)$ conformal coset
theories, are investigated in conjunction with the string black hole solution.
The angular variable in the Euclidean version, is found to have a double set of
winding. Region III is shown to be $SU(2)_k/U(1)$ where the doubling accounts
for the cut sructure of the parafermionic amplitudes and fits nicely across the
horizon and singularity. The implications for string thermodynamics and
identical particles correlations are discussed.
| 1991-08-21
| 2007-05-23
|
[
"hep-th"
] |
Mordechai Spiegelglas
|
hep-th/9108011
|
Twisted Black p-Brane Solutions in String Theory
|
It has been shown that given a classical background in string theory which is
independent of $d$ of the space-time coordinates, we can generate other
classical backgrounds by $O(d)\otimes O(d)$ transformation on the solution. We
study the effect of this transformation on the known black $p$-brane solutions
in string theory, and show how these transformations produce new classical
solutions labelled by extra continuous parameters and containing background
antisymmetric tensor field.
| 1991-08-21
| 2009-09-15
|
[
"hep-th"
] |
Ashoke Sen
|
hep-th/9108008
|
Novel Symmetries of Topological Conformal Field theories
|
We show that various actions of topological conformal theories that were
suggested recentely are particular cases of a general action. We prove the
invariance of these models under transformations generated by nilpotent
fermionic generators of arbitrary conformal dimension, $\Q$ and $\G$. The later
are shown to be the $n^{th}$ covariant derivative with respect to ``flat
abelian gauge field" of the fermionic fields of those models. We derive the
bosonic counterparts $\W$ and $\R$ which together with $\Q$ and $\G$ form a
special $N=2$ super $W_\infty$ algebra. The algebraic structure is discussed
and it is shown that it generalizes the so called ``topological algebra".
| 1991-08-20
| 2007-05-23
|
[
"hep-th"
] |
J. Sonnenschein and S. Yankielowicz
|
hep-th/9108009
|
Solving 3+1 QCD on the Transverse Lattice Using 1+1 Conformal Field
Theory
|
A new transverse lattice model of $3+1$ Yang-Mills theory is constructed by
introducing Wess-Zumino terms into the 2-D unitary non-linear sigma model
action for link fields on a 2-D lattice. The Wess-Zumino terms permit one to
solve the basic non-linear sigma model dynamics of each link, for discrete
values of the bare QCD coupling constant, by applying the representation theory
of non-Abelian current (Kac-Moody) algebras. This construction eliminates the
need to approximate the non-linear sigma model dynamics of each link with a
linear sigma model theory, as in previous transverse lattice formulations. The
non-perturbative behavior of the non-linear sigma model is preserved by this
construction. While the new model is in principle solvable by a combination of
conformal field theory, discrete light-cone, and lattice gauge theory
techniques, it is more realistically suited for study with a Tamm-Dancoff
truncation of excited states. In this context, it may serve as a useful
framework for the study of non-perturbative phenomena in QCD via analytic
techniques.
| 1991-08-20
| 2009-10-22
|
[
"hep-th"
] |
Paul A. Griffin
|
hep-th/9108006
|
Discrete and Continuum Approaches to Three-Dimensional Quantum Gravity
|
It is shown that, in the three-dimensional lattice gravity defined by Ponzano
and Regge, the space of physical states is isomorphic to the space of
gauge-invariant functions on the moduli space of flat $SU(2)$ connections over
a two-dimensional surface, which gives physical states in the $ISO(3)$
Chern-Simons gauge theory.
| 1991-08-20
| 2009-09-17
|
[
"hep-th"
] |
Hirosi Ooguri and Naoki Sasakura
|
hep-th/9108007
|
Infinite Quantum Group Symmetry of Fields in Massive 2D Quantum Field
Theory
|
Starting from a given S-matrix of an integrable quantum field theory in $1+1$
dimensions, and knowledge of its on-shell quantum group symmetries, we describe
how to extend the symmetry to the space of fields. This is accomplished by
introducing an adjoint action of the symmetry generators on fields, and
specifying the form factors of descendents. The braiding relations of quantum
field multiplets is shown to be given by the universal $\CR$-matrix. We develop
in some detail the case of infinite dimensional Yangian symmetry. We show that
the quantum double of the Yangian is a Hopf algebra deformation of a level zero
Kac-Moody algebra that preserves its finite dimensional Lie subalgebra. The
fields form infinite dimensional Verma-module representations; in particular
the energy-momentum tensor and isotopic current are in the same multiplet.
| 1991-08-20
| 2015-06-26
|
[
"hep-th"
] |
A. LeCLair and F. Smirnov
|
hep-th/9108005
|
Fusion Residues
|
We discuss when and how the Verlinde dimensions of a rational conformal field
theory can be expressed as correlation functions in a topological LG theory. It
is seen that a necessary condition is that the RCFT fusion rules must exhibit
an extra symmetry. We consider two particular perturbations of the Grassmannian
superpotentials. The topological LG residues in one perturbation, introduced by
Gepner, are shown to be a twisted version of the $SU(N)_k$ Verlinde dimensions.
The residues in the other perturbation are the twisted Verlinde dimensions of
another RCFT; these topological LG correlation functions are conjectured to be
the correlation functions of the corresponding Grassmannian topological sigma
model with a coupling in the action to instanton number.
| 1991-08-19
| 2015-06-26
|
[
"hep-th"
] |
Kenneth Intriligator
|
hep-th/9108004
|
Ground Ring Of Two Dimensional String Theory
|
String theories with two dimensional space-time target spaces are
characterized by the existence of a ``ground ring'' of operators of spin
$(0,0)$. By understanding this ring, one can understand the symmetries of the
theory and illuminate the relation of the critical string theory to matrix
models. The symmetry groups that arise are, roughly, the area preserving
diffeomorphisms of a two dimensional phase space that preserve the fermi
surface (of the matrix model) and the volume preserving diffeomorphisms of a
three dimensional cone. The three dimensions in question are the matrix
eigenvalue, its canonical momentum, and the time of the matrix model.
| 1991-08-16
| 2010-04-07
|
[
"hep-th"
] |
Edward Witten
|
hep-th/9108002
|
Hamiltonian construction of W-gravity actions
|
We show that all W-gravity actions can be easilly constructed and understood
from the point of view of the Hamiltonian formalism for the constrained
systems. This formalism also gives a method of constructing gauge invariant
actions for arbitrary conformally extended algebras.
| 1991-08-15
| 2009-01-16
|
[
"hep-th"
] |
A. Mikovic
|
hep-th/9108003
|
Supersymmetric Gelfand-Dickey Algebra
|
We study the classical version of supersymmetric $W$-algebras. Using the
second Gelfand-Dickey Hamiltonian structure we work out in detail $W_2$ and
$W_3$-algebras.
| 1991-08-15
| 2015-06-26
|
[
"hep-th"
] |
Katri Huitu and Dennis Nemeschansky
|
hep-th/9108001
|
Exact Black String Solutions in Three Dimensions
|
A family of exact conformal field theories is constructed which describe
charged black strings in three dimensions. Unlike previous charged black hole
or extended black hole solutions in string theory, the low energy spacetime
metric has a regular inner horizon (in addition to the event horizon) and a
timelike singularity. As the charge to mass ratio approaches unity, the event
horizon remains but the singularity disappears.
| 1991-08-14
| 2009-10-22
|
[
"hep-th"
] |
James H. Horne and Gary T. Horowitz
|
math/9201305
|
Alternating sign matrices and domino tilings
|
We introduce a family of planar regions, called Aztec diamonds, and study the
ways in which these regions can be tiled by dominoes. Our main result is a
generating function that not only gives the number of domino tilings of the
Aztec diamond of order $n$ but also provides information about the orientation
of the dominoes (vertical versus horizontal) and the accessibility of one
tiling from another by means of local modifications. Several proofs of the
formula are given. The problem turns out to have connections with the
alternating sign matrices of Mills, Robbins, and Rumsey, as well as the square
ice model studied by Lieb.
| 1991-06-01
| 2008-02-03
|
[
"math.CO"
] |
Noam Elkies (Harvard), Greg Kuperberg (UC Berkeley), Michael Larsen (U
Penn), James Propp (MIT)
|
math/9201299
|
Geometric finiteness and uniqueness for Kleinian groups with circle
packing limit sets
|
In this paper, we assume that $G$ is a finitely generated torsion free
non-elementary Kleinian group with $\Omega(G)$ nonempty. We show that the
maximal number of elements of $G$ that can be pinched is precisely the maximal
number of rank 1 parabolic subgroups that any group isomorphic to $G$ may
contain. A group with this largest number of rank 1 maximal parabolic subgroups
is called {\it maximally parabolic}. We show such groups exist. We state our
main theorems concisely here.
Theorem I. The limit set of a maximally parabolic group is a circle packing;
that is, every component of its regular set is a round disc.
Theorem II. A maximally parabolic group is geometrically finite.
Theorem III. A maximally parabolic pinched function group is determined up to
conjugacy in $PSL(2,{\bf C})$ by its abstract isomorphism class and its
parabolic elements.
| 1991-12-11
| 2016-09-06
|
[
"math.DG",
"math.GT"
] |
Linda Keen, Bernard Maskit, Caroline Series
|
math/9201298
|
On removable sets for Sobolev spaces in the plane
|
Let $K$ be a compact subset of $\bar{\bold C} ={\bold R}^2$ and let $K^c$
denote its complement. We say $K\in HR$, $K$ is holomorphically removable, if
whenever $F:\bar{\bold C} \to\bar{\bold C}$ is a homeomorphism and $F$ is
holomorphic off $K$, then $F$ is a M\"obius transformation. By composing with a
M\"obius transform, we may assume $F(\infty )=\infty$. The contribution of this
paper is to show that a large class of sets are $HR$. Our motivation for these
results is that these sets occur naturally (e.g. as certain Julia sets) in
dynamical systems, and the property of being $HR$ plays an important role in
the Douady-Hubbard description of their structure.
| 1991-11-26
| 2016-09-06
|
[
"math.DS"
] |
Peter Jones
|
math/9201297
|
Periodic orbits for Hamiltonian systems in cotangent bundles
|
We prove the existence of at least $cl(M)$ periodic orbits for certain time
dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact
manifold $M$. These Hamiltonians are not necessarily convex but they satisfy a
certain boundary condition given by a Riemannian metric on $M$. We discretize
the variational problem by decomposing the time 1 map into a product of
``symplectic twist maps''. A second theorem deals with homotopically non
trivial orbits in manifolds of negative curvature.
| 1991-11-11
| 2008-02-03
|
[
"math.DS"
] |
Christopher Gol\'e
|
math/9201296
|
On the realization of fixed point portraits (an addendum to Goldberg,
Milnor: Fixed point portraits)
|
We establish that every formal critical portrait (as defined by Goldberg and
Milnor), can be realized by a postcritically finite polynomial.
| 1991-10-27
| 2008-02-03
|
[
"math.DS"
] |
Alfredo Poirier
|
math/9201294
|
On the quasisymmetrical classification of infinitely renormalizable
maps: I. Maps with Feigenbaum's topology.
|
A semigroup (dynamical system) generated by $C^{1+\alpha}$-contracting
mappings is considered. We call a such semigroup regular if the maximum $K$ of
the conformal dilatations of generators, the maximum $l$ of the norms of the
derivatives of generators and the smoothness $\alpha$ of the generators satisfy
a compatibility condition $K< 1/l^{\alpha}$. We prove the {\em geometric
distortion lemma} for a regular semigroup generated by
$C^{1+\alpha}$-contracting mappings.
| 1991-10-11
| 2016-09-06
|
[
"math.DS"
] |
Yunping Jiang
|
math/9201295
|
On the quasisymmetrical classification of infinitely renormalizable
maps: II. remarks on maps with a bounded type topology.
|
We use the upper and lower potential functions and Bowen's formula estimating
the Hausdorff dimension of the limit set of a regular semigroup generated by
finitely many $C^{1+\alpha}$-contracting mappings. This result is an
application of the geometric distortion lemma in the first paper at this
series.
| 1991-10-11
| 2016-09-06
|
[
"math.DS"
] |
Yunping Jiang
|
math/9201293
|
Dynamics of certain non-conformal degree two maps on the plane
|
In this paper we consider maps on the plane which are similar to quadratic
maps in that they are degree 2 branched covers of the plane. In fact, consider
for $\alpha$ fixed, maps $f_c$ which have the following form (in polar
coordinates):
$$f_c(r\,e^{i\theta})\;=\;r^{2\alpha}\,e^{2i\theta}\,+\,c$$
When $\alpha=1$, these maps are quadratic ($z \maps z^2 + c$), and their
dynamics and bifurcation theory are to some degree understood. When $\alpha$ is
different from one, the dynamics is no longer conformal. In particular, the
dynamics is not completely determined by the orbit of the critical point.
Nevertheless, for many values of the parameter c, the dynamics has strong
similarities to that of the quadratic family. For other parameter values the
dynamics is dominated by 2 dimensional behavior: saddles and the like.
The objects of study are Julia sets, filled-in Julia sets and the
connectedness locus. These are defined in analogy to the conformal case. The
main drive in this study is to see to what extent the results in the conformal
case generalize to that of maps which are topologically like quadratic maps
(and when $\alpha$ is close to one, close to being quadratic).
| 1991-09-26
| 2011-07-26
|
[
"math.DS"
] |
Ben Bielefeld, Scott Sutherland, Folkert Tangerman, J. J. P. Veerman
|
math/9201292
|
Quasisymmetric conjugacies between unimodal maps
|
It is shown that some topological equivalency classes of S-unimodal maps are
equal to quasisymmetric conjugacy classes. This includes some infinitely
renormalizable polynomials of unbounded type.
| 1991-08-27
| 2009-09-25
|
[
"math.DS"
] |
Michael Jakobson, Grzegorz Swiatek
|
math/9201291
|
The Fibonacci unimodal map
|
This paper will study topological, geometrical and measure-theoretical
properties of the real Fibonacci map. Our goal was to figure out if this type
of recurrence really gives any pathological examples and to compare it with the
infinitely renormalizable patterns of recurrence studied by Sullivan. It turns
out that the situation can be understood completely and is of quite regular
nature. In particular, any Fibonacci map (with negative Schwarzian and
non-degenerate critical point) has an absolutely continuous invariant measure
(so, we deal with a ``regular'' type of chaotic dynamics). It turns out also
that geometrical properties of the closure of the critical orbit are quite
different from those of the Feigenbaum map: its Hausdorff dimension is equal to
zero and its geometry is not rigid but depends on one parameter.
| 1991-08-12
| 2016-09-06
|
[
"math.DS"
] |
Mikhail Lyubich, John W. Milnor
|
math/9201290
|
The "spectral" decomposition for one-dimensional maps
|
We construct the "spectral" decomposition of the sets $\bar{Per\,f}$,
$\omega(f)=\cup\omega(x)$ and $\Omega(f)$ for a continuous map $f$ of the
interval to itself. Several corollaries are obtained; the main ones describe
the generic properties of $f$-invariant measures, the structure of the set
$\Omega(f)\setminus \bar{Per\,f}$ and the generic limit behavior of an orbit
for maps without wandering intervals. The "spectral" decomposition for
piecewise-monotone maps is deduced from the Decomposition Theorem. Finally we
explain how to extend the results of the present paper for a continuous map of
a one-dimensional branched manifold into itself.
| 1991-07-27
| 2016-01-25
|
[
"math.DS"
] |
Alexander M. Blokh
|
math/9201289
|
Periods implying almost all periods, trees with snowflakes, and zero
entropy maps
|
Let $X$ be a compact tree, $f$ be a continuous map from $X$ to itself,
$End(X)$ be the number of endpoints and $Edg(X)$ be the number of edges of $X$.
We show that if $n>1$ has no prime divisors less than $End(X)+1$ and $f$ has a
cycle of period $n$, then $f$ has cycles of all periods greater than
$2End(X)(n-1)$ and topological entropy $h(f)>0$; so if $p$ is the least prime
number greater than $End(X)$ and $f$ has cycles of all periods from 1 to
$2End(X)(p-1)$, then $f$ has cycles of all periods (this verifies a conjecture
of Misiurewicz for tree maps). Together with the spectral decomposition theorem
for graph maps it implies that $h(f)>0$ iff there exists $n$ such that $f$ has
a cycle of period $mn$ for any $m$. We also define {\it snowflakes} for tree
maps and show that $h(f)=0$ iff every cycle of $f$ is a snowflake or iff the
period of every cycle of $f$ is of form $2^lm$ where $m\le Edg(X)$ is an odd
integer with prime divisors less than $End(X)+1$.
| 1991-07-12
| 2016-01-25
|
[
"math.DS"
] |
Alexander M. Blokh
|
math/9201287
|
Dynamics of certain smooth one-dimensional mappings III: Scaling
function geometry
|
We study scaling function geometry. We show the existence of the scaling
function of a geometrically finite one-dimensional mapping. This scaling
function is discontinuous. We prove that the scaling function and the
asymmetries at the critical points of a geometrically finite one-dimensional
mapping form a complete set of $C^{1}$-invariants within a topological
conjugacy class.
| 1991-06-27
| 2008-02-03
|
[
"math.DS"
] |
Yunping Jiang
|
math/9201288
|
Dynamics of certain smooth one-dimensional mappings IV: Asymptotic
geometry of Cantor sets
|
We study hyperbolic mappings depending on a parameter $\varepsilon $. Each of
them has an invariant Cantor set. As $\varepsilon $ tends to zero, the mapping
approaches the boundary of hyperbolicity. We analyze the asymptotics of the gap
geometry and the scaling function geometry of the invariant Cantor set as
$\varepsilon $ goes to zero. For example, in the quadratic case, we show that
all the gaps close uniformly with speed $\sqrt {\varepsilon}$. There is a
limiting scaling function of the limiting mapping and this scaling function has
dense jump discontinuities because the limiting mapping is not expanding.
Removing these discontinuities by continuous extension, we show that we obtain
the scaling function of the limiting mapping with respect to the Ulam-von
Neumann type metric.
| 1991-06-27
| 2016-09-06
|
[
"math.DS"
] |
Yunping Jiang
|
math/9201286
|
Ergodic theory for smooth one-dimensional dynamical systems
|
In this paper we study measurable dynamics for the widest reasonable class of
smooth one dimensional maps. Three principle decompositions are described in
this class : decomposition of the global measure-theoretical attractor into
primitive ones, ergodic decomposition and Hopf decomposition. For maps with
negative Schwarzian derivative this was done in the series of papers [BL1-BL5],
but the approach to the general smooth case must be different.
| 1991-06-12
| 2016-09-06
|
[
"math.DS"
] |
Mikhail Lyubich
|
math/9201285
|
On the Lebesgue measure of the Julia set of a quadratic polynomial
|
The goal of this note is to prove the following theorem: Let $p_a(z) = z^2+a$
be a quadratic polynomial which has no irrational indifferent periodic points,
and is not infinitely renormalizable. Then the Lebesgue measure of the Julia
set $J(p_a)$ is equal to zero.
As part of the proof we discuss a property of the critical point to be {\it
persistently recurrent}, and relate our results to corresponding ones for real
one dimensional maps. In particular, we show that in the persistently recurrent
case the restriction $p_a|\omega(0)$ is topologically minimal and has zero
topological entropy. The Douady-Hubbard-Yoccoz rigidity theorem follows this
result.
| 1991-05-28
| 2016-09-06
|
[
"math.DS"
] |
Mikhail Lyubich
|
math/9201284
|
The Teichm\"uller space of an Anosov diffeomorphism of $T^2$
|
In this paper we consider the space of smooth conjugacy classes of an Anosov
diffeomorphism of the two-torus. The only 2-manifold that supports an Anosov
diffeomorphism is the 2-torus, and Franks and Manning showed that every such
diffeomorphism is topologically conjugate to a linear example, and furthermore,
the eigenvalues at periodic points are a complete smooth invariant. The
question arises: what sets of eigenvalues occur as the Anosov diffeomorphism
ranges over a topological conjugacy class? This question can be reformulated:
what pairs of cohomology classes (one determined by the expanding eigenvalues,
and one by the contracting eigenvalues) occur as the diffeomorphism ranges over
a topological conjugacy class? The purpose of this paper is to answer this
question: all pairs of H\"{o}lder reduced cohomology classes occur.
| 1991-05-12
| 2016-09-06
|
[
"math.DS"
] |
Elise E. Cawley
|
math/9201283
|
Critical circle maps near bifurcation
|
We estimate harmonic scalings in the parameter space of a one-parameter
family of critical circle maps. These estimates lead to the conclusion that the
Hausdorff dimension of the complement of the frequency-locking set is less than
$1$ but not less than $1/3$. Moreover, the rotation number is a H\"{o}lder
continuous function of the parameter.
| 1991-04-27
| 2016-09-06
|
[
"math.DS"
] |
Jacek Graczyk, Grzegorz Swiatek
|
math/9201282
|
The Hausdorff dimension of the boundary of the Mandelbrot set and Julia
sets
|
It is shown that the boundary of the Mandelbrot set $M$ has Hausdorff
dimension two and that for a generic $c \in \bM$, the Julia set of $z \mapsto
z^2+c$ also has Hausdorff dimension two. The proof is based on the study of the
bifurcation of parabolic periodic points.
| 1991-04-12
| 2016-09-06
|
[
"math.DS"
] |
Mitsuhiro Shishikura
|
math/9201281
|
Expanding direction of the period doubling operator
|
We prove that the period doubling operator has an expanding direction at the
fixed point. We use the induced operator, a ``Perron-Frobenius type operator'',
to study the linearization of the period doubling operator at its fixed point.
We then use a sequence of linear operators with finite ranks to study this
induced operator. The proof is constructive. One can calculate the expanding
direction and the rate of expansion of the period doubling operator at the
fixed point.
| 1991-03-28
| 2016-09-06
|
[
"math.DS"
] |
Yunping Jiang, Takehiko Morita, Dennis Sullivan
|
math/9201280
|
Polynomial root-finding algorithms and branched covers
|
We construct a family of root-finding algorithms which exploit the branched covering structure of a polynomial of degree $d$ with a path-lifting algorithm for finding individual roots. In particular, the family includes an algorithm that computes an $ε$-factorization of the polynomial which has an arithmetic complexity of $\Order{d^2(\log d)^2 + d(\log d)^2|\logε|}$. At the present time (1993), this complexity is the best known in terms of the degree.
| 1991-03-13
| 2025-10-20
|
[
"math.DS",
"cs.NA",
"math.NA"
] |
Myong-Hi Kim, Scott Sutherland
|
math/9201279
|
A partial description of the parameter space of rational maps of degree
two: Part 2
|
This continues the investigation of a combinatorial model for the variation
of dynamics in the family of rational maps of degree two, by concentrating on
those varieties in which one critical point is periodic. We prove some general
results about nonrational critically finite degree two branched coverings, and
finally identify the boundary of the rational maps in the combinatorial model,
thus completing the proofs of results announced in Part 1.
| 1991-02-25
| 2009-09-25
|
[
"math.DS"
] |
Mary Rees
|
math/9201277
|
Dynamics of certain smooth one-dimensional mappings I: The
$C^{1+\alpha}$-Denjoy-Koebe distortion lemma
|
We prove a technical lemma, the $C^{1+\alpha }$-Denjoy-Koebe distortion
lemma, estimating the distortion of a long composition of a $C^{1+\alpha }$
one-dimensional mapping $f:M\mapsto M$ with finitely many, non-recurrent, power
law critical points. The proof of this lemma combines the ideas of the
distortion lemmas of Denjoy and Koebe.
| 1991-01-11
| 2016-09-06
|
[
"math.DS"
] |
Yunping Jiang
|
math/9201278
|
Dynamics of certain smooth one-dimensional mappings II: geometrically
finite one-dimensional mappings
|
We study geometrically finite one-dimensional mappings. These are a subspace
of $C^{1+\alpha}$ one-dimensional mappings with finitely many, critically
finite critical points. We study some geometric properties of a mapping in this
subspace. We prove that this subspace is closed under quasisymmetrical
conjugacy. We also prove that if two mappings in this subspace are
topologically conjugate, they are then quasisymmetrically conjugate. We show
some examples of geometrically finite one-dimensional mappings.
| 1991-01-11
| 2008-02-03
|
[
"math.DS"
] |
Yunping Jiang
|
math/9201236
|
On certain classes of Baire-1 functions with applications to Banach
space theory
|
Certain subclasses of $B_1(K)$, the Baire-1 functions on a compact metric
space $K$, are defined and characterized. Some applications to Banach spaces
are given.
| 1991-12-31
| 2009-09-25
|
[
"math.FA"
] |
Richard Haydon, Edward Odell, and Haskell P. Rosenthal
|
math/9201235
|
On the distribution of Sidon series
|
Let B denote an arbitrary Banach space, G a compact abelian group with Haar
measure $\mu$ and dual group $\Gamma$. Let E be a Sidon subset of $\Gamma$ with
Sidon constant S(E). Let r_n denote the n-th Rademacher function on [0, 1]. We
show that there is a constant c, depending only on S(E), such that, for all
$\alpha > 0$: c^{-1}P[| \sum_{n=1}^Na_nr_n| >= c \alpha ] <= \mu[|
\sum_{n=1}^Na_n\gamma_n| >= \alpha ] <= cP [|\sum_{n=1}^Na_nr_n| >= c^{-1}
\alpha ]
| 1991-12-10
| 2008-02-03
|
[
"math.FA"
] |
Nakhl\'e Asmar and Stephen J. Montgomery-Smith
|
math/9201234
|
Analytic Disks in Fibers over the Unit Ball of a Banach Space
|
We study biorthogonal sequences with special properties, such as weak or
weak-star convergence to 0, and obtain an extension of the Josefson-Nissenzweig
theorem. This result is applied to embed analytic disks in the fiber over 0 of
the spectrum of H^infinity (B), the algebra of bounded analytic functions on
the unit ball B of an arbitrary infinite dimensional Banach space. Various
other embedding theorems are obtained. For instance, if the Banach space is
superreflexive, then the unit ball of a Hilbert space of uncountable dimension
can be embedded analytically in the fiber over 0 via an embedding which is
uniformly bicontinuous with respect to the Gleason metric.
| 1991-10-11
| 2016-09-06
|
[
"math.FA"
] |
B. J. Cole, T. W. Gamelin, William B. Johnson
|
math/9201233
|
On J. Borwein's concept of sequentially reflexive Banach spaces
|
A Banach space $X$ is reflexive if the Mackey topology $\tau(X^*,X)$ on $X^*$
agrees with the norm topology on $X^*$. Borwein [B] calls a Banach space $X$
{\it sequentially reflexive\/} provided that every $\tau(X^*,X)$ convergent
{\it sequence\/} in $X^*$ is norm convergent. The main result in [B] is that
$X$ is sequentially reflexive if every separable subspace of $X$ has separable
dual, and Borwein asks for a characterization of sequentially reflexive spaces.
Here we answer that question by proving
\proclaim Theorem. {\sl A Banach space $X$ is sequentially reflexive if and
only if $\ell_1$ is not isomorphic to a subspace of $X$.}
| 1991-10-09
| 2016-09-06
|
[
"math.FA"
] |
Peter {\O}rno
|
math/9201232
|
The K_t-functional for the interpolation couple L_1(A_0),L_infinity(A_1)
|
Let (A_0,A_1) be a compatible couple of Banach spaces in the interpolation
theory sense. We give a formula for the K_t-functional of the interpolation
couples (l_1(A_0),c_0(A_1)) or (l_1(A_0),l_infinity(A_1)) and
(L_1(A_0),L_infinity(A_1)).
| 1991-09-21
| 2008-02-03
|
[
"math.FA"
] |
Gilles Pisier
|
math/9201230
|
Banach spaces with Property (w)
|
A Banach space E is said to have Property (w) if every (bounded linear)
operator from E into E' is weakly compact. We give some interesting examples of
James type Banach spaces with Property (w). We also consider the passing of
Property (w) from E to C(K,E).
| 1991-07-24
| 2016-09-06
|
[
"math.FA"
] |
Denny H. Leung
|
math/9201231
|
A Gordon-Chevet type Inequality
|
We prove a new inequality for Gaussian processes, this inequality implies the
Gordon-Chevet inequality. Some remarks on Gaussian proofs of Dvoretzky's
theorem are given.
| 1991-07-24
| 2009-09-25
|
[
"math.FA"
] |
B. Khaoulani
|
math/9201229
|
Interpolation between H^p spaces and non-commutative generalizations, I
|
We give an elementary proof that the $H^p$ spaces over the unit disc (or the
upper half plane) are the interpolation spaces for the real method of
interpolation between $H^1$ and $H^\infty$. This was originally proved by Peter
Jones. The proof uses only the boundedness of the Hilbert transform and the
classical factorisation of a function in $H^p$ as a product of two functions in
$H^q$ and $H^r$ with $1/q+1/r=1/p$. This proof extends without any real extra
difficulty to the non-commutative setting and to several Banach space valued
extensions of $H^p$ spaces. In particular, this proof easily extends to the
couple $H^{p_0}(\ell_{q_0}),H^{p_1}(\ell_{q_1})$, with $1\leq p_0, p_1, q_0,
q_1 \leq \infty$. In that situation, we prove that the real interpolation
spaces and the K-functional are induced ( up to equivalence of norms ) by the
same objects for the couple $L_{p_0}(\ell_{q_0}), L_{p_1}(\ell_{q_1})$. In
another direction, let us denote by $C_p$ the space of all compact operators
$x$ on Hilbert space such that $tr(|x|^p) <\infty$. Let $T_p$ be the subspace
of all upper triangular matrices relative to the canonical basis. If
$p=\infty$, $C_p$ is just the space of all compact operators. Our proof allows
us to show for instance that the space $H^p(C_p)$ (resp. $T_p$) is the
interpolation space of parameter $(1/p,p)$ between $H^1(C_1)$ (resp. $T_1$) and
$H^\infty(C_\infty)$ (resp. $T_\i$). We also prove a similar result for the
complex interpolation method. Moreover, extending a recent result of
Kaftal-Larson and Weiss, we prove that the distance to the subspace of upper
triangular matrices in $C_1$ and $C_\infty$ can be essentially realized
simultaneously by the same element.
| 1991-06-04
| 2008-02-03
|
[
"math.FA"
] |
Gilles Pisier
|
math/9201228
|
A simple proof of a theorem of Jean Bourgain
|
We give a simple proof of Bourgain's disc algebra version of Grothendieck's
theorem, i.e. that every operator on the disc algebra with values in $L_1$ or
$L_2$ is 2-absolutely summing and hence extends to an operator defined on the
whole of $C$. This implies Bourgain's result that $L_1/H^1$ is of cotype 2. We
also prove more generally that $L_r/H^r$ is of cotype 2 for $0<r< 1$.
| 1991-06-03
| 2009-09-25
|
[
"math.FA"
] |
Gilles Pisier
|
math/9201226
|
Interpolation of operators when the extreme spaces are $L^\infty$
|
In this paper, equivalence between interpolation properties of linear
operators and monotonicity conditions are studied, for a pair $(X_0,X_1)$ of
rearrangement invariant quasi Banach spaces, when the extreme spaces of the
interpolation are $L^\infty$ and a pair $(A_0,A_1)$ under some assumptions.
Weak and restricted weak intermediate spaces fall in our context. Applications
to classical Lorentz and Lorentz-Orlicz spaces are given.
| 1991-04-29
| 2008-02-03
|
[
"math.FA"
] |
Jes\'us Bastero and Francisco J. Ruiz
|
math/9201225
|
An arbitrarily distortable Banach space
|
In this work we construct a ``Tsirelson like Banach space'' which is
arbitrarily distortable.
| 1991-04-03
| 2007-06-13
|
[
"math.FA"
] |
Thomas Schlumprecht
|
math/9201224
|
On Schreier unconditional sequences
|
Let $(x_n)$ be a normalized weakly null sequence in a Banach space and let
$\varep>0$. We show that there exists a subsequence $(y_n)$ with the following
property: $$\hbox{ if }\ (a_i)\subseteq \IR\ \hbox{ and }\ F\subseteq \nat$$
satisfies $\min F\le |F|$ then $$\big\|\sum_{i\in F} a_i y_i\big\| \le
(2+\varep) \big\| \sum a_iy_i\big\|\ . $$
| 1991-03-22
| 2008-02-03
|
[
"math.FA"
] |
Edward Odell
|
math/9201222
|
Non dentable sets in Banach spaces with separable dual
|
A non RNP Banach space E is constructed such that $E^{*}$ is separable and
RNP is equivalent to PCP on the subsets of E.
| 1991-02-05
| 2009-09-25
|
[
"math.FA"
] |
Spiros A. Argyros, Irene Deliyanni
|
math/9201223
|
Level sets and the uniqueness of measures
|
A result of Nymann is extended to show that a positive $\sigma$-finite
measure with range an interval is determined by its level sets. An example is
given of two finite positive measures with range the same finite union of
intervals but with the property that one is determined by its level sets and
the other is not.
| 1991-02-05
| 2008-02-03
|
[
"math.FA"
] |
Dale E. Alspach
|
math/9201221
|
Comparison of Orlicz-Lorentz spaces
|
Orlicz-Lorentz spaces provide a common generalization of Orlicz spaces and
Lorentz spaces. They have been studied by many authors, including Masty\l o,
Maligranda, and Kami\'nska. In this paper, we consider the problem of comparing
the Orlicz-Lorentz norms, and establish necessary and sufficient conditions for
them to be equivalent. As a corollary, we give necessary and sufficient
conditions for a Lorentz-Sharpley space to be equivalent to an Orlicz space,
extending results of Lorentz and Raynaud. We also give an example of a
rearrangement invariant space that is not an Orlicz-Lorentz space.
| 1991-01-02
| 2008-02-03
|
[
"math.FA"
] |
Stephen J. Montgomery-Smith
|
math/9201304
|
Efficient representation of perm groups
|
This note presents an elementary version of Sims's algorithm for computing
strong generators of a given perm group, together with a proof of correctness
and some notes about appropriate low-level data structures. Upper and lower
bounds on the running time are also obtained. (Following a suggestion of
Vaughan Pratt, we adopt the convention that perm $=$ permutation, perhaps
thereby saving millions of syllables in future research.)
| 1991-01-01
| 2008-02-03
|
[
"math.GR"
] |
Donald E. Knuth
|
math/9201247
|
On a conjecture of Tarski on products of cardinals
|
We look at an old conjecture of A. Tarski on cardinal arithmetic and show
that if a counterexample exists, then there exists one of length omega_1 +
omega .
| 1991-01-15
| 2009-09-25
|
[
"math.LO"
] |
Thomas Jech, Saharon Shelah
|
math/9201248
|
A partition theorem for pairs of finite sets
|
Every partition of [[omega_1]^{< omega}]^2 into finitely many pieces has a
cofinal homogeneous set. Furthermore, it is consistent that every directed
partially ordered set satisfies the partition property if and only if it has
finite character.
| 1991-01-15
| 2008-02-03
|
[
"math.LO"
] |
Thomas Jech, Saharon Shelah
|
math/9201246
|
The primal framework. II. Smoothness
|
This is the second in a series of articles developing abstract classification
theory for classes that have a notion of prime models over independent pairs
and over chains. It deals with the problem of smoothness and establishing the
existence and uniqueness of a `monster model'. We work here with a predicate
for a canonically prime model.
| 1991-01-15
| 2016-09-06
|
[
"math.LO"
] |
John T. Baldwin, Saharon Shelah
|
math/9201243
|
The Hanf numbers of stationary logic. II. Comparison with other logics
|
We show that the ordering of the Hanf number of L_{omega, omega}(wo) (well
ordering), L^c_{omega, omega} (quantification on countable sets), L_{omega,
omega}(aa) (stationary logic) and second order logic, have no more restraints
provable in ZFC than previously known (those independence proofs assume
CON(ZFC) only). We also get results on corresponding logics for L_{lambda, mu} .
| 1991-01-15
| 2013-10-22
|
[
"math.LO"
] |
Saharon Shelah
|
math/9201245
|
Viva la difference I: Nonisomorphism of ultrapowers of countable models
|
We show that it is not provable in ZFC that any two countable elementarily
equivalent structures have isomorphic ultrapowers relative to some ultrafilter
on omega .
| 1991-01-15
| 2008-02-03
|
[
"math.LO"
] |
Saharon Shelah
|
math/9201244
|
Strong partition relations below the power set: consistency, was
Sierpinski right, II?
|
We continue here [She88] but we do not rely on it. The motivation was a
conjecture of Galvin stating that 2^{omega} >= omega_2 + omega_2->
[omega_1]^{n}_{h(n)} is consistent for a suitable h: omega-> omega. In section
5 we disprove this and give similar negative results. In section 3 we prove the
consistency of the conjecture replacing omega_2 by 2^omega, which is quite
large, starting with an Erd\H{o}s cardinal. In section 1 we present iteration
lemmas which are needed when we replace omega by a larger lambda and in section
4 we generalize a theorem of Halpern and Lauchli replacing omega by a larger
lambda .
| 1991-01-15
| 2024-01-30
|
[
"math.LO"
] |
Saharon Shelah
|
math/9201227
|
Remarks on complemented subspaces of von-Neumann algebras
|
In this note we include two remarks about bounded ($\underline{not}$
necessarily contractive) linear projections on a von Neumann-algebra. We show
that if $M$ is a von Neumann-subalgebra of $B(H)$ which is complemented in B(H)
and isomorphic to $M \otimes M$ then $M$ is injective (or equivalently $M$ is
contractively complemented). We do not know how to get rid of the second
assumption on $M$. In the second part,we show that any complemented reflexive
subspace of a $C^*$- algebra is necessarily linearly isomorphic to a Hilbert
space.
| 1991-05-31
| 2009-09-25
|
[
"math.OA",
"math.FA"
] |
Gilles Pisier
|
math/9201302
|
The quantum G_2 link invariant
|
We derive an inductive, combinatorial definition of a polynomial-valued
regular isotopy invariant of links and tangled graphs. We show that the
invariant equals the Reshetikhin-Turaev invariant corresponding to the
exceptional simple Lie algebra G_2. It is therefore related to G_2 in the same
way that the HOMFLY polynomial is related to A_n and the Kauffman polynomial is
related to B_n, C_n, and D_n. We give parallel constructions for the other rank
2 Lie algebras and present some combinatorial conjectures motivated by the new
inductive definitions.
| 1991-10-07
| 2016-09-06
|
[
"math.QA",
"math.GT"
] |
Greg Kuperberg (U Chicago)
|
alg-geom/9212004
|
Automorphisms and the K\"ahler cone of certain Calabi-Yau manifolds
|
For the Calabi-Yau threefolds $X$ constructed by C. Schoen as fiber products
of generic rational elliptic surfaces, we show that the action of the
automorphism group of $X$ on the K\"ahler cone of $X$ has a rationally
polyhedral fundamental domain. The second author has conjectured that this
statement will hold in general, the example presented here being the first
non-trivial case in which the statement has been checked. The conjecture was
motivated by the desire to use a construction of E. Looijenga to compactify
certain moduli spaces which arise in the study of conformal field theory and
``mirror symmetry.''
| 1992-12-22
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Antonella Grassi and David R. Morrison
|
alg-geom/9212003
|
The enumeration of simultaneous higher-order contacts between plane
curves
|
Using the Semple bundle construction, we derive an intersection-theoretic
formula for the number of simultaneous contacts of specified orders between
members of a generic family of degree $d$ plane curves and finitely many fixed
curves. The contacts counted by the formula occur at nonsingular points of both
the members of the family and the fixed curves.
| 1992-12-08
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Susan Jane Colley and Gary Kennedy
|
alg-geom/9212002
|
On the stable rationality of $X/G$
|
Let $G$ be a connected, reductive algeraic group whose Dynkin diagram
contains no components of type $G_2,$ $F_4,$ $E_6,$ $E_7$ or $E_8.$ That is,
all the components are of classical type. Suppose $X$ is an affine variety, and
suppose $G$ acts freely on $X.$ Then $X$ and $X/G$ are stably birationally
equivalent.
| 1992-12-04
| 2012-01-20
|
[
"alg-geom",
"math.AG"
] |
Amnon Neeman
|
alg-geom/9212001
|
Algebraic approximations of holomorphic maps from Stein domains to
projective manifolds
|
It is shown that every holomorphic map $f$ from a Runge domain $\Omega$ of an
affine algebraic variety $S$ into a projective algebraic manifold $X$ is a
uniform limit of Nash algebraic maps $f_\nu$ defined over an exhausting
sequence of relatively compact open sets $\Omega_\nu$ in $\Omega$. A relative
version is also given: If there is an algebraic subvariety $A$ (not necessarily
reduced) in $S$ such that the restriction of $f$ to $A\cap\Omega$ is algebraic,
then $f_\nu$ can be taken to coincide with $f$ on $A\cap\Omega_\nu$. The main
application of these results, when $\Omega$ is the unit disk, is to show that
the Kobayashi pseudodistance and the Kobayashi-Royden infinitesimal metric of a
quasi-projective algebraic manifold $Z$ are computable solely in terms of the
closed algebraic curves in $Z$. Similarly, the $p$-dimensional Eisenman metric
of a quasi-projective algebraic manifold can be computed in terms of the
Eisenman volumes of its $p$-dimensional algebraic subvarieties. Another
question addressed in the paper is whether the approximations $f_\nu$ can be
taken to have their images contained in affine Zariski open subsets of $X$. By
using complex analytic methods (pluricomplex potential theory and H\"ormander's
$L^2$ estimates), we show that this is the case if $f$ is an embedding (with
$\dim S<\dim X$) and if there is an ample line bundle $L$ on $X$ such that
| 1992-12-01
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Jean-Pierre Demailly, Laszlo Lempert and Bernard Shiffman
|
alg-geom/9211001
|
Stable pairs on curves and surfaces
|
We describe stability conditions for pairs consisting of a coherent sheaf and
a homomorphism to a fixed coherent sheaf on a projective variety. The
corresponding moduli spaces are constructed for pairs on curves and surfaces.
We consider two examples. The fixed sheaf is the structure sheaf or is a vector
bundle on a divisor, i.e. Higgs pairs or framed bundles, resp. (unencoded
version)
| 1992-11-09
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Daniel Huybrechts and Manfred Lehn
|
alg-geom/9210009
|
Elliptic Three-folds I: Ogg-Shafarevich Theory
|
We calculate the Tate-Shafarevich group of an elliptic three-fold
$f:X\rightarrow S$ when $X$ and $S$ are regular and $f$ is flat, relating it to
the Brauer group of $X$ and $S$. We show that given certain hypotheses on $f$,
the Tate-Shafarevich group has the interpretation of isomorphism classes of
elliptic curves over the function field of $S$ which have the same jacobian as
the generic fibre of $f$, and for which there exists a relatively minimal model
which has no multiple fibres. We use this to give examples of elliptic
fibrations with isolated multiple fibres, and also to give a new counterexample
to the Luroth problem in dimension three. This is a revised, hopefully
improved, version with a few extra theorems and a few errors corrected.
| 1992-10-30
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
I. Dolgachev and M. Gross
|
alg-geom/9210008
|
Erratum to "The Homogeneous Coordinate Ring of a Toric Variety", along
with the original paper
|
This submission consists of two papers: 1) an erratum that corrects an error
in the proof of Proposition 4.3 in my paper "The Homogeneous Coordinate Ring of
a Toric Variety", and 2) the original (unchanged) version of the paper,
published in 1995. The original paper introduced the homogeneous coordinate
ring of a toric variety (now called the total coordinate ring or Cox ring) and
gave a quotient construction. The paper also studied sheaves on a toric
variety, and in Section 4 described its automorphism group. The error in the
proof of Proposition 4.3 resulted from the faulty assumption that a certain set
of graded endomorphisms forms a ring; rather, it is a monoid under composition.
The erratum notes this error and gives a correct proof of the proposition.
| 1992-10-22
| 2014-03-07
|
[
"alg-geom",
"math.AG"
] |
David A. Cox (Amherst College)
|
alg-geom/9210007
|
Stable pairs, linear systems and the Verlinde formula
|
We study the moduli problem of pairs consisting of a rank 2 vector bundle and
a nonzero section over a fixed smooth curve. The stability condition involves a
parameter; as it varies, we show that the moduli space undergoes a sequence of
flips in the sense of Mori. As applications, we prove several results about
moduli spaces of rank 2 bundles, including the Harder-Narasimhan formula and
the SU(2) Verlinde formula. Indeed, we prove a general result on the space of
sections of powers of the ideal sheaf of a curve in projective space, which
includes the Verlinde formula.
| 1992-10-19
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Michael Thaddeus
|
alg-geom/9210006
|
Reductive group actions on K\"ahler manifolds
|
We prove that the action of a reductive complex Lie group on a K\"ahler
manifold can be linearized in the neighbourhood of a fixed point, provided that
the restriction of the action to some compact real form of the group is
Hamiltonian with respect to the K\"ahler form.
| 1992-10-14
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Eugene Lerman and Reyer Sjamaar
|
alg-geom/9210005
|
Degrees of Curves in Abelian Varieties
|
The degree of a curve $C$ in a polarized abelian variety $(X,\lambda)$ is the
integer $d=C\cdot\lambda$. When $C$ generates $X$, we find a lower bound on $d$
which depends on $n$ and the degree of the polarization $\lambda$. The smallest
possible degree is $d=n$ and is obtained only for a smooth curve in its
Jacobian with its principal polarization (Ran, Collino). The cases $d=n+1$ and
$d=n+2$ are studied. Moreover, when $X$ is simple, it is shown, using results
of Smyth on the trace of totally positive algebraic integers, that if $d\le
1.7719\, n$, then $C$ is smooth and $X$ is isomorphic to its Jacobian. We also
get an upper bound on the geometric genus of $C$ in terms of its degree.
| 1992-10-13
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Olivier Debarre
|
alg-geom/9210004
|
Points of Low Degree on Smooth Plane Curves
|
The purpose of this note is to provide some applications of Faltings' recent
proof of S. Lang's conjecture to smooth plane curves. Let $C$ be a smooth plane
curve defined by an equation of degree $d$ with integral coefficients. We show
that for $d\ge 7$, the curve $C$ has only finitely many points whose field of
definition has degree $\le d-2$ over $Q$, and that for $d\ge 8$, all but
finitely many points of $C$ whose field of definition has degree $\le d-1$ over
$Q$ arise as points of intersection of rational lines through rational points
of $C$.
| 1992-10-13
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Olivier Debarre and Matthew Klassen
|
alg-geom/9210003
|
The simple method of distinguishing the underlying differentiable
structures of algebraic surfaces
|
The simplest version of the Spin-polynomial invariants of the underlying
differentiable structures of algebraic surfaces were considered and the
simplest arguments were used in order to distinguish the underlying smooth
structures of certain algebraic surfaces.
| 1992-10-10
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
Andrej Tyurin
|
alg-geom/9210002
|
Chow quotients of Grassmannian I
|
We introduce a certain compactification of the space of projective
configurations i.e. orbits of the group $PGL(k)$ on the space of $n$ - tuples
of points in $P^{k-1}$ in general position. This compactification differs
considerably from Mumford's geometric invariant theory quotient. It is obtained
by considering limit position (in the Chow variety) of the closures of generic
orbits. The same result will be obtained if we study orbits of the maximal
torus on the Grassmannian $G(k,n)$. We study in detail the closures of the
torus orbits and their "visible contours" which are Veronese varieties in the
Grassmannian. For points on $P^1$ our construction gives the Grothemdieck -
Knudsen moduli space of stable $n$ -punctured curves of genus 0. The "Chow
quotient" interpretation of this space permits us to represent it as a blow up
of a projective space.
| 1992-10-07
| 2008-02-03
|
[
"alg-geom",
"math.AG"
] |
M.Kapranov
|
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