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300 | On the cohomology of SL(2,Z[1/p]) | math.AT | In this paper we compute the integral cohomology of the discrete groups
SL(2,Z[1/p]), where p is any prime. | math |
301 | On Combinatorial Descriptions of Homotopy Groups of $ΣK(π,1)$ | math.AT | We give a combinatorial description of homotopy groups of $\Sigma K(\pi,1)$.
In particular, all of the homotopy groups of the $3$-sphere are combinatorially
given. | math |
302 | On the Homology of Configuration Spaces $C((M,M_o)\times {\bold R}^n; X)$ | math.AT | The homology with coefficients in a field of the configuration spaces
$C(M\times \bold R ^n,M_o\times \bold R ^n;X)$ is determined in this paper. | math |
303 | On Combinatorial Calculations for the James--Hopf maps | math.AT | We give some formulas of the James-Hopf maps by using combinatorial methods.
An application is to give a product decomposition of the spaces
$\Omega\Sigma^2(X)$. | math |
304 | A Product Decomposition of $Ω^3_0Σ${\bf R}$P^2$ | math.AT | We give a specific product decomposition of the base-point path connected
component of the triple loop space of the suspension of the projective plane. | math |
305 | Homotopy Lie groups | math.AT | Homotopy Lie groups, recently invented by W.G. Dwyer and C.W. Wilkerson,
represent the culmination of a long evolution. The basic philosophy behind the
process was formulated almost 25 years ago by Rector in his vision of a
homotopy theoretic incarnation of Lie group theory. What was then technically
impossible has now... | math |
306 | Topological transformation groups | math.AT | This paper surveys some results and methods in topological transformation
groups. | math |
307 | The combinatorics of Steenrod operations on the cohomology of Grassmannians | math.AT | The study of the action of the Steenrod algebra on the mod $p$ cohomology of
spaces has many applications to the topological structure of those spaces. In
this paper we present combinatorial formulas for the action of Steenrod
operations on the cohomology of Grassmannians, both in the Borel and the
Schubert picture. We... | math |
308 | Symmetric spectra | math.AT | The long hunt for a symmetric monoidal category of spectra finally ended in
success with the simultaneous discovery of the third author's discovery of
symmetric spectra and the Elmendorf-Kriz-Mandell-May category of S-modules. In
this paper we define and study the model category of symmetric spectra, based
on simplicia... | math |
309 | Symmetric ring spectra and topological Hochschild homology | math.AT | Symmetric spectra were introduced by Jeff Smith as a symmetric monoidal
category of spectra. In this paper, a detection functor is defined which
detects stable equivalences of symmetric spectra. This detection functor is
useful because the classic stable homotopy groups do not detect stable
equivalences in symmetric sp... | math |
310 | Algebras and modules in monoidal model categories | math.AT | We construct model category structures for monoids and modules in symmetric
monoidal model categories which satisfy an extra axiom, the monoidal axiom,
with applications to symmetric spectra and $\Gamma$-spaces. | math |
311 | The structure of the Bousfield lattice | math.AT | Using Ohkawa's theorem that the collection of Bousfield classes is a set, we
perform a number of constructions with Bousfield classes. In particular, we
describe a greatest lower bound operator; we also note that a certain subset DL
of the Bousfield lattice is a frame, and we examine some consequences of this
observati... | math |
312 | Morava E-theory of symmetric groups | math.AT | We compute the completed E(n) cohomology of the classifying spaces of the
symmetric groups, and relate the answer to the theory of finite subgroups of
formal groups. | math |
313 | Phantom Maps and Homology Theories | math.AT | We study phantom maps and homology theories in a stable homotopy category S
via a certain Abelian category A. We express the group P(X,Y) of phantom maps X
-> Y as an Ext group in A, and give conditions on X or Y which guarantee that
it vanishes. We also determine P(X,HB). We show that any composite of two
phantom maps... | math |
314 | Monoidal model categories | math.AT | A monoidal model category is a model category with a compatible closed
monoidal structure. Such things abound in nature; simplicial sets and chain
complexes of abelian groups are examples. Given a monoidal model category, one
can consider monoids and modules over a given monoid. We would like to be able
to study the ho... | math |
315 | Loop spaces and homotopy operations | math.AT | The question of whether a given H-space X is, up to homotopy, a loop space
has been studied from a variety of viewpoints. Here we address this question
from the aspect of homotopy operations, in the classical sense of operations on
homotopy groups.
First, we show how an H-space structure on X can be used to define th... | math |
316 | Vanishing lines in Adams spectral sequences are generic | math.AT | We show that in a generalized Adams spectral sequence, the presence of a
vanishing line of fixed slope (at some term of the spectral sequence, with some
intercept) is a generic property. | math |
317 | Some new embeddings and nonimmersions of real projective spaces | math.AT | We use obstruction theory to prove that if alpha(n)=2, then RP^{16n+8} cannot
be immersed in R^{32n+3} and RP^{16n+10} cannot be immersed in R^{32n+11}, and
that if alpha(n)>2, then RP^{8n+4} can be embedded in R^{16n+1}. These are new
results. | math |
318 | 3-primary v1-periodic homotopy groups of E7 | math.AT | We compute the 3-primary v1-periodic homotopy groups of the exceptional Lie
group E7. Now E8 at the primes 3 and 5 is the only compact simple Lie group
whose odd-primary v1-periodic homotopy groups remian to be computed. The main
work is computing the unstable Novikov spectral sequence of \Omega E7/Sp(2).
Showing that ... | math |
319 | A Lefschetz type coincidence theorem | math.AT | A Lefschetz-type coincidence theorem for two maps f,g:X->Y from an arbitrary
topological space X to a manifold Y is given: I(f,g)=L(f,g), the coincidence
index is equal to the Lefschetz number. It follows that if L(f,g) is not equal
to zero then there is an x in X such that f(x)=g(x). In particular, the theorem
contain... | math |
320 | Spaces of polynomials with roots of bounded multiplicity | math.AT | We describe an alternative approach to some results of Vassiliev on spaces of
polynomials, by using the scanning method which was used by Segal in his
investigation of spaces of rational functions. We explain how these two
approaches are related by the Smale-Hirsch Principle or the h-Principle of
Gromov. We obtain seve... | math |
321 | Ideals in Triangulated Categories: Phantoms, Ghosts and Skeleta | math.AT | We begin by showing that in a triangulated category, specifying a projective
class is equivalent to specifying an ideal I of morphisms with certain
properties, and that if I has these properties, then so does each of its
powers. We show how a projective class leads to an Adams spectral sequence and
give some results on... | math |
322 | Constructions of E_n Operads | math.AT | This paper discusses the question of how to recognize whether an operad is
E_n (ie. equivalent to the little n-cubes operad). A construction is given
which produces many new examples of E_n operads. This construction is developed
in the context of an infinite family of right adjoint constructions for
operads. Some othe... | math |
323 | Homotopy Algebras via Resolutions of Operads | math.AT | The aim of this brief note is mainly to advocate our approach to homotopy
algebras based on the minimal model of an operad. Our exposition is motivated
by two examples which we discuss very explicitly - the example of strongly
homotopy associative algebras and the example of strongly homotopy Lie
algebras.
We then in... | math |
324 | Completions of Z/(p)-Tate cohomology of periodic spectra | math.AT | We construct splittings of some completions of the Z/(p)-Tate cohomology of
E(n) and some related spectra. In particular, we split (a completion of) tE(n)
as a (completion of) a wedge of E(n-1)'s as a spectrum, where t is shorthand
for the fixed points of the Z/(p)-Tate cohomology spectrum (ie Mahowald's
inverse limit ... | math |
325 | m-structures determine integral homotopy type | math.AT | This paper proves that the functor $C(*)$ that sends pointed,
simply-connected CW-complexes to their chain-complexes equipped with diagonals
and iterated higher diagonals, determines their integral homotopy type --- even
inducing an equivalence of categories between the category of CW-complexes up
to homotopy equivalen... | math |
326 | Algebraic Shifting Increases Relative Homology | math.AT | \newcommand{\rhomi}[1]{\widetilde{H}_{#1}} \newcommand{\rbeti}[1]{\beta_{#1}}
\newcommand{\kk}{\mathbf k} \newcommand{\dimk}{\dim_{\kk}}
We show that algebraically shifting a pair of simplicial complexes weakly
increases their relative homology Betti numbers in every dimension.
More precisely, let $\Delta(K)$ denot... | math |
327 | An Interpolation between Homology and Stable Homotopy | math.AT | By considering labeled configurations of ``bounded multiplicity'', one can
construct a functor that fits between homology and stable homotopy. Based on
previous work, we are able to give an equivalent description of this labeled
construction in terms of loop space functors and symmetric products. This
yields a direct g... | math |
328 | On the nonexistence of Smith-Toda complexes | math.AT | Let p be a prime. The Smith-Toda complex V(k) is a finite spectrum whose
BP-homology is isomorphic to BP_*/(p,v_1,...,v_k). For example, V(-1) is the
sphere spectrum and V(0) the mod p Moore spectrum. In this paper we show that
if p > 5, then V((p+3)/2) does not exist and V((p+1)/2), if it exists, is not a
ring spectru... | math |
329 | Phantom maps and chromatic phantom maps | math.AT | In the first part, we determine conditions on spectra X and Y under which
either every map from X to Y is phantom, or no nonzero maps are. We also
address the question of whether such all or nothing behaviour is preserved when
X is replaced with V smash X for V finite. In the second part, we introduce
chromatic phantom... | math |
330 | Algebraic invariants for homotopy types | math.AT | We define inductively a sequence of purely algebraic invariants - namely,
classes in the Quillen cohomology of the Pi-algebra \pi_* X - for
distinguishing between different homotopy types of spaces. Another sequence of
such cohomology classes allows one to decide whether a given abstract
Pi-algebra can be realized as t... | math |
331 | On the relation between lifting obstructions and ordinary obstructions | math.AT | We consider partial liftings of maps at fibrations and compare the primary
obstruction to extend the lifting with the obstruction to extend the lifting as
a simple map into the total space. A relation between these two obstructions is
proved for the case when the fiber is an Eilenberg-MacLane space. Furthermore
it is s... | math |
332 | On the cohomology of Galois groups determined by Witt rings | math.AT | Let F denote a field of characteristic different from two. In this paper we
describe the mod 2 cohomology of a Galois group which is determined by the Witt
ring WF. | math |
333 | Exponents and the cohomology of finite groups | math.AT | Provides a counterexample to a long standing conjecture of A. Adem regarding
the behaviour of the integral cohomology of a p-group. | math |
334 | A degree one Borsuk-Ulam theorem | math.AT | We observe that the classical Borsuk-Ulam theorem has an easy generalization
to maps from an n-manifold M^n to R^n. We point out a geometric corollary. | math |
335 | Configuration spaces with summable labels | math.AT | Let M be an n-manifold, and let A be a space with a partial sum behaving as
an n-fold loop sum. We define the space C(M;A) of configurations in M with
summable labels in A via operad theory. Some examples are symmetric products,
labelled configuration spaces, and spaces of rational curves.
We show that C(I^n,dI^n;A) ... | math |
336 | Forgetable map and phantom maps | math.AT | In this note, we attack a question posed ten years ago by Tsukiyama about the
injectivity of the so- called Forgetable map. We show that we can insert the
Forgetable map in an exact sequence and that the problem can be reduced to the
computation of the sequence which turns out unexpectedly to be related to the
phantom ... | math |
337 | Homotopy Algebras are Homotopy Algebras | math.AT | We prove that strongly homotopy algebras (such as $A_\infty$, $C_\infty$, sh
Lie, $B_\infty$, $G_\infty$,...) are homotopically invariant in the category of
chain complexes. An important consequence is a rigorous proof that `strongly
homotopy structures transfer over chain homotopy equivalences.' | math |
338 | Vanishing lines in generalized Adams spectral sequences are generic | math.AT | We show that in a generalized Adams spectral sequence, the presence of a
vanishing line of fixed slope (at some term of the spectral sequence, with some
intercept) is a generic property. | math |
339 | On the cobordism classification of manifolds with Z/p-action | math.AT | We refer to an action of the group Z/p (p here is an odd prime) on a stably
complex manifold as simple if all its fixed submanifolds have the trivial
normal bundle. The important particular case of a simple action is an action
with only isolated fixed points. The problem of cobordism classification of
manifolds with si... | math |
340 | Lefschetz Coincidence Theory for Maps Between Spaces of Different Dimensions | math.AT | For a given pair of maps f,g:X->M from an arbitrary topological space to an
n-manifold, the Lefschetz homomorphism is a certain graded homomorphism
L:H(X)->H(M) of degree (-n). We prove a Lefschetz-type coincidence theorem: if
the Lefschetz homomorphism is nontrivial then there is an x in X such that
f(x)=g(x). | math |
341 | The 1-line of the K-theory Bousfield-Kan spectral sequence for Spin(2n+1) | math.AT | For X a simply-connected finite H-space, there is a Bousfield-Kan spectral
sequence which converges to the homotopy of its K-completion. When
X=Spin(2n+1), we expect that these homotopy groups equal the v1-periodic
homotopy groups in dimension greater than n^2. In this paper, we accomplish two
things. (1) We prove that... | math |
342 | Computations of Complex Equivariant Bordism Rings | math.AT | In this paper we compute homotopical bordism rings $MU^G_*$ for abelian
compact Lie groups G, giving explicit generators and relations. The key
constructions are operations on equivariant bordism which should play an
important role in equivariant stable homotopy theory more generally. The main
technique used is localiz... | math |
343 | Transversality Obstructions and Equivariant Bordism for G=Z/2 | math.AT | In this paper we compute homotopical equivariant bordism for the group ${\bf
Z/2}$, namely $MO^{\bf Z/2}$, geometric equivariant bordism $\Omega^{\bf
Z/2}_*$, and their quotient as modules over geometric bordism. This quotient is
a module of stable transversality obstructions. In doing these computations, we
use the te... | math |
344 | Equivariant Elliptic Cohomology and Rigidity | math.AT | Equivariant elliptic cohomology with complex coefficients was defined
axiomatically by Ginzburg, Kapranov and Vasserot and constructed by Grojnowski.
We give an invariant definition of S^1-equivariant elliptic cohomology, and use
it to give an entirely cohomological proof of the rigidity theorem of Witten
for the ellip... | math |
345 | Realizing coalgebras over the Steenrod algebra | math.AT | We describe algebraic obstruction theories for realizing an abstract
coalgebra K_* over the mod p Steenrod algebra as the homology of a topological
space, and for distinguishing between the p-homotopy types of different
realizations. The theories are expressed in terms of the Quillen cohomology of
K_*. | math |
346 | CW simplicial resolutions of spaces, with an application to loop spaces | math.AT | We show how a certain type of CW simplicial resolutions of space by wedges of
spheres may be constructed for any topological space, and how such resolutions
yield an obstruction theory for a given space X to be a loop space. | math |
347 | Extension dimension and C-spaces | math.AT | Some generalizations of the classical Hurewicz formula are obtained for
extension dimension and C-spaces. | math |
348 | The toric cobordisms | math.AT | A smooth closed 3-manifold $M$ fibered by tori $T^2$ is characterized by an
element $\phi \in GL(2,\mathbb{Z})$. We show that $M$ is the boundary of a
4-manifold fibered by tori over a surface such that the bundle structure on $M$
is the restriction of the bundle structure on the 4-manifold if and only if
$\phi$ is fro... | math |
349 | Ideal Perturbation Lemma | math.AT | We explain the essence of perturbation problems. The key to understanding is
the structure of chain homotopy equivalence -- the standard one must be
replaced by a finer notion which we call a strong chain homotopy equivalence.
We prove an Ideal Perturbation Lemma and show how both new and classical
results follow from ... | math |
350 | An Index of an Equivariant Vector Field and Addition Theorems for Pontrjagin Characteristic Classes | math.AT | The theory of indices of Morse--Bott vector fields on a manifold is
constructed and the famous localization problem for the transfer map is solved
on its base in the present paper. As a consequence, we obtained addition
theorems for the universal Pontrjagin characteristic classes in cobordisms.
These results gave us a ... | math |
351 | Characteristic Classes for GO(2n,C) | math.AT | The complex Lie group GO(2n,C) by definition consists of all complex matrices
A of size 2n, such that A times transpose(A) is a non-zero scalar. In this
paper we determine explicitly the singular cohomology ring of the classifying
space BGO(2n,C) with mod 2 coefficients, in terms of generators and relations.
The method... | math |
352 | Operads and algebraic homotopy | math.AT | This paper proves that the homotopy type of a pointed, simply-connected,
2-reduced simplicial set is determined by the chain-complex augmented by
functorial diagonal and higher diagonal maps (a simple generalization of the
ones used to define Steenrod operations). The treatment of this problem is
completely self-contai... | math |
353 | Dickson Invariants in the image of the Steenrod Square | math.AT | Let D_n be the Dickson invariant ring of F_2[X_1,...,X_n] acted by the
general linear group GL(n,\F_2). In this paper, we provide an elementary proof
of the conjecture by [Hung]: each element in D_n is in the image of the
Steenrod square in F_2[X_1,...,X_n], where n>3. | math |
354 | Absolute non-Archimedean polyhedral expansions of ultrauniform spaces | math.AT | This work is devoted to the investigation of the problem about inverse
mapping systems expansions of ultrauniform spaces $X$ using polyhedra over
non-Archimedean locally compact fields $\bf L$. Theorems about expansions of
complete ultrametric and ultrauniform spaces are proved. Absolute polyhedral
expansions and inver... | math |
355 | On commuting and non-commuting complexes | math.AT | In this paper we study various simplicial complexes associated to the
commutative structure of a finite group G. We define NC(G) (resp. C(G)) as the
complex associated to the poset of pairwise non-commuting (resp. commuting)
sets in G.
We observe that NC(G) has only one positive dimensional connected component,
which... | math |
356 | Combinatorial model categories have presentations | math.AT | We show that every combinatorial model category can be obtained, up to
Quillen equivalence, by localizing a model category of diagrams of simplicial
sets. This says that any combinatorial model category can be built up from a
category of `generators' and a set of `relations'---that is, any combinatorial
model category ... | math |
357 | The Witten genus and equivariant elliptic cohomology | math.AT | We construct a Thom class in complex equivariant elliptic cohomology
extending the equivariant Witten genus. This gives a new proof of the rigidity
of the Witten genus, which exhibits a close relationship to recent work on
non-equivariant orientations of elliptic spectra. | math |
358 | The cohomology ring of free loop spaces | math.AT | Let X be a simply connected space and k a commutative ring. Goodwillie,
Burghelea and Fiedorowiscz proved that the Hochschild cohomology of the
singular chains on the pointed loop space HH^{*}S_*(\Omega X) is isomorphic to
the free loop space cohomology H^{*}(X^{S^{1}}). We proved that this
isomorphism is compatible wi... | math |
359 | The homology of iterated loop spaces | math.AT | The singular chain complex of the iterated loop space is expressed in terms
of the cobar construction. After that we consider the spectral sequence of the
cobar construction and calculate its first term over Z/p-coefficients and over
a field of characteristic zero. Finally we apply these results to calculate the
homolo... | math |
360 | Subgroups of the group of self-homotopy equivalences | math.AT | Denote by E(Y) the group of homotopy classes of self-homotopy equivalences of
a finite-dimensional complex Y. We give a selection of results about certain
subgroups of E(Y). We establish a connection between the Gottlieb groups of Y
and the subgroup of E(Y) consisting of homotopy classes of self-homotopy
equivalences t... | math |
361 | Variations on a conjecture of Halperin | math.AT | Halperin has conjectured that the Serre spectral sequence of any fibration
that has fibre space a certain kind of elliptic space should collapse at the
E_2-term. In this paper we obtain an equivalent phrasing of this conjecture, in
terms of formality relations between base and total spaces in such a fibration
(Theorem ... | math |
362 | Rational obstruction theory and rational homotopy sets | math.AT | We develop an obstruction theory for homotopy of homomorphisms f,g : M -> N
between minimal differential graded algebras. We assume that M = Lambda V has
an obstruction decomposition given by V = V_0 oplus V_1 and that f and g are
homotopic on Lambda V_0. An obstruction is then obtained as a vector space
homomorphism V... | math |
363 | Stasheff structures and differentials of the Adams spectral sequence | math.AT | The Adams spectral sequence was invented by J.F.Adams almost fifty years ago
for calculations of stable homotopy groups of topological spaces and in
particular of spheres. The calculation of differentials of this spectral
sequence is one of the most difficult problem of Algebraic Topology. Here we
consider an approach ... | math |
364 | A Diagonal on the Associahedra | math.AT | Let C_*(K) denote the cellular chains on the Stasheff associahedra. We
construct an explicit combinatorial diagonal \Delta : C_*(K) --> C_*(K) \otimes
C_*(K); consequently, we obtain an explicit diagonal on the A_\infty-operad. We
apply the diagonal \Delta to define the tensor product of A_\infty-(co)algebras
in maxima... | math |
365 | Gross-Hopkins duality | math.AT | We give a new and simpler proof of a result of Hopkins and Gross relating
Brown-Comenetz duality to Spanier-Whitehead duality in the K(n)-local stable
homotopy category. | math |
366 | K(n)-local duality for finite groups and groupoids | math.AT | We define an inner product (suitably interpreted) on the K(n)-local spectrum
LG := L_{K(n)}BG_+, where G is a finite group or groupoid. This gives an inner
product on E^*BG_+ for suitable K(n)-local ring spectra E. We relate this to
the usual inner product on the representation ring when n=1, and to the
Hopkins-Kuhn-Ra... | math |
367 | The BP<n> cohomology of elementary abelian groups | math.AT | In this paper we study E^*BV_k, where E=BP<m,n> is a cohomology theory with
coefficient ring F_p[v_m,...,v_n] (if m>0) or Z_(p)[v_1,...,v_n] (if m=0). We
use ideas from the theory of multiple level structures, developed in earlier
work of the author with John Greenlees. Our results apply when k is less than
or equal to... | math |
368 | Formal schemes and formal groups | math.AT | We set up a framework for using algebraic geometry to study the generalised
cohomology rings that occur in algebraic topology. This idea was probably first
introduced by Quillen and it underlies much of our understanding of complex
oriented cohomology theories, exemplified by the work of Morava. Most of the
results hav... | math |
369 | Products on MU-modules | math.AT | We use the new categories of spectra and MU-modules constructed by Elmendorf,
Kriz, Mandell and May to get improved results about multiplicative structures
on spectra such as P(n) and E(n), particularly in the case p=2. | math |
370 | Common subbundles and intersections of divisors | math.AT | Let V_0 and V_1 be complex vector bundles over a space X. We use the theory
of divisors on formal groups to give obstructions in generalised cohomology
that vanish when V_0 and V_1 can be embedded in a bundle U in such a way that
V_0\cap V_1 has dimension at least k everywhere. We study various algebraic
universal exam... | math |
371 | The Hopf Rings for KO and KU | math.AT | We compute the mod two homology Hopf rings of the spectra KO and KU. The
spaces in these spectra are the infinite classical groups and their coset
spaces, and their homology was first calculated in the Cartan seminars, but the
Hopf ring structure was first determined in the second author's unpublished PhD
thesis. The p... | math |
372 | On the Topology of Fibrations with Section and Free Loop Spaces | math.AT | We relate the brace products of a fibration with section to the differentials
in its serre spectral sequence. In the particular case of free loop fibrations,
we establish a link between these differentials and browder operations in the
fiber. Applications and several calculations (for the particular case of
spheres and... | math |
373 | A uniqueness theorem for stable homotopy theory | math.AT | In this paper we study the global structure of the stable homotopy theory of
spectra. We establish criteria for when the homotopy theory associated to a
given stable model category agrees with the classical stable homotopy theory of
spectra. One sufficient condition is that the associated homotopy category is
equivalen... | math |
374 | Monoidal uniqueness theorems for stable homotopy theory | math.AT | We show that the monoidal product on the stable homotopy category of spectra
is essentially unique. This strengthens work of this author with Schwede on the
uniqueness of models of the stable homotopy theory of spectra. As an
application we show that with an added assumption about underlying model
structures Margolis' ... | math |
375 | The Whitehead group of the Novikov ring | math.AT | The Bass-Heller-Swan-Farrell-Hsiang-Siebenmann decomposition of the Whitehead
group $K_1(A_{\rho}[z,z^{-1}])$ of a twisted Laurent polynomial extension
$A_{\rho}[z,z^{-1}]$ of a ring $A$ is generalized to a decomposition of the
Whitehead group $K_1(A_{\rho}((z)))$ of a twisted Novikov ring of power series
$A_{\rho}((z)... | math |
376 | Automorphisms of manifolds | math.AT | This is a survey paper on spaces of automorphisms of manifolds and spaces of
manifolds in a fixed homotopy type. It describes the main theorems of
traditional surgery theory, but also the main theorems of pseudoisotopy theory,
alias concordance theory, Waldhausen style. It culminates in (an outline of) a
synthesis of t... | math |
377 | Equivariant Cohomology and Representations of the Symmetric Group | math.AT | A cohomological study is made of an equivariant map betwen the configuration
space of n points in space and the flag manifold of U(n). | math |
378 | Morse theory for the Yang-Mills functional via equivariant homotopy theory | math.AT | In this paper we show the existence of non minimal critical points of the
Yang-Mills functional over a certain family of 4-manifolds with generic
SU(2)-invariant metrics using Morse and homotopy theoretic methods. These
manifolds are acted on fixed point freely by the Lie group SU(2) with quotient
a compact Riemann sur... | math |
379 | Simplicial structures on model categories and functors | math.AT | We produce a highly structured way of associating a simplicial category to a
model category which improves on work of Dwyer and Kan and answers a question
of Hovey. We show that model categories satisfying a certain axiom are Quillen
equivalent to simplicial model categories. A simplicial model category provides
higher... | math |
380 | P-th powers in mod p cohomology of fibers | math.AT | Let $F\hookrightarrow E\twoheadrightarrow B$ be a fibration whose base space
$B$ is a finite simply-connected CW-complex of dimension $\leq p$ and whose
total space $E$ is a path-connected CW-complex of dimension $\leq p-1$. If
$\alpha\in H^{+}(F;\mathbb{F}_p)$ then $\alpha ^{p}=0$. | math |
381 | Supplement to the paper "Floating bundles and their applications" | math.AT | This paper is the supplement to the section 2 of the paper "Floating bundles
and their applications" (math.AT/0102054). Below we construct the denumerable
set of extensions of the formal group of geometric cobordisms $F(x\otimes
1,1\otimes x)$ by the Hopf algebra $H=\Omega_U^*(Gr).$ | math |
382 | Homotopy Diagrams of Algebras | math.AT | In [math.AT/9907138] we proved that strongly homotopy algebras are homotopy
invariant concepts in the category of chain complexes. Our arguments were based
on the fact that strongly homotopy algebras are algebras over minimal cofibrant
operads and on the principle that algebras over cofibrant operads are homotopy
invar... | math |
383 | A Torsion-Free Milnor-Moore Theorem | math.AT | Let \Omega X be the space of Moore loops on a finite, q-connected,
n-dimensional CW complex X, and let R be a subring of Q containing 1/2. Let
p(R) be the least non-invertible prime in R. For a graded R-module M of finite
type, let FM = M / Torsion M. We show that the inclusion of the sub-Lie algebra
P of primitive ele... | math |
384 | On Brown-Peterson cohomology of QX | math.AT | We compute the Brown-Peterson cohomology of QX, the free infinite loop-space
on X, when X is a space whose Morava K-theory is flat over its BP-cohomology,
in particular a space whose Morava K-theory is concentrated in even degrees.
Our computation is in terms of a destabilization functor for BP-cohomology. We
also show... | math |
385 | Supplement 2 to the paper "Floating bundles and their applications" | math.AT | This paper is the supplement to the section 2 of the paper "Floating bundles
and their applications" (math.AT/0102054). Below we study some properties of
category, connected with cobordism rings of FBSP. In particular, we shall show
that it is the tensor category. | math |
386 | Logarithms of formal groups over Hopf algebras | math.AT | The aim of this paper is to prove the following result. For any commutative
formal group ${\frak F}(x\otimes 1,1\otimes x),$ which is considered as a
formal group over $H_\mathbb{Q},$ there exists a homomorphism to a formal group
of the form ${\frak c}+x\otimes 1+1\otimes x,$ where $\frak c\in
H_\mathbb{Q}{\mathop{\hat... | math |
387 | Filtered Topological Cyclic Homology and relative K-theory of nilpotent ideals | math.AT | In this paper we examine certain filtrations of topological Hochschild
homology and topological cyclic homology. As an example we show how the
filtration with respect to a nilpotent ideal gives rise to an analog of a
theorem of Goodwillie saying that rationally relative K-theory and relative
cyclic homology agree. Our ... | math |
388 | Clapp-Puppe Type Lusternik-Schnirelmann (Co)category in a Model Category | math.AT | We introduce Clapp-Puppe type generalized Lusternik-Schnirelmann (co)category
in a Quillen model category. We establish some of their basic properties and
give various characterizations of them. As the first application of these
characterizations, we show that our generalized (co)category is invariant under
Quillen mod... | math |
389 | On the Adams Spectral Sequence for R-modules | math.AT | We discuss the Adams Spectral Sequence for R-modules based on commutative
localized regular quotient ring spectra over a commutative S-algebra R in the
sense of Elmendorf, Kriz, Mandell, May and Strickland. The formulation of this
spectral sequence is similar to the classical case and the calculation of its
E_2-term in... | math |
390 | On adic genus, Postnikov conjugates, and lambda-rings | math.AT | Sufficient conditions on a space are given which guarantee that the
$K$-theory ring and the ordinary cohomology ring with coefficients over a
principal ideal domain are invariants of, respectively, the adic genus and the
SNT set. An independent proof of Notbohm's theorem on the classification of the
adic genus of $BS^3... | math |
391 | On Kan fibrations for Maltsev algebras | math.AT | We prove that any surjective homomorphism of simplicial Maltsev algebras is a
Kan fibration. | math |
392 | A model structure on the category of pro-simplicial sets | math.AT | We study the category pro-SSet of pro-simplicial sets, which arises in etale
homotopy theory, shape theory, and pro-finite completion. We establish a model
structure on pro-SSet so that it is possible to do homotopy theory in this
category. This model structure is closely related to the strict structure of
Edwards and ... | math |
393 | Coarse homology theories | math.AT | In this paper we develop an axiomatic approach to coarse homology theories.
We prove a uniqueness result concerning coarse homology theories on the
category of `coarse CW-complexes'. This uniqueness result is used to prove a
version of the coarse Baum-Connes conjecture for such spaces. | math |
394 | Homotopy classes that are trivial mod F | math.AT | If F is a collection of topological spaces, then a homotopy class \alpha in
[X,Y] is called F-trivial if \alpha_* = 0: [A,X] --> [A,Y] for all A in F. In
this paper we study the collection Z_F(X,Y) of all F-trivial homotopy classes
in [X,Y] when F = S, the collection of spheres, F = M, the collection of Moore
spaces, a... | math |
395 | A remark on the genus of the infinite quaternionic projective space | math.AT | It is shown that only countably many spaces in the genus of $\hpinfty$, the
infinite quaternionic projective space, can admit essential maps from
$\cpinfty$, the infinite complex projective space. Examples of countably many
homotopically distinct spaces in the genus of $\hpinfty$ which admit essential
maps from $\cpinf... | math |
396 | Secondary Brown-Kervaire Quadratic forms and $π$-manifolds | math.AT | In this paper we define a secondary Brown-Kervaire quadratic forms. Among the
applications we obtain a complete classification of (n-2)-connected
2n-dimensional framed manifolds up to homeomorphism and homotopy equivalence, .
In particular, we prove that the homotopy type of such manifolds determine
their homeomorphism... | math |
397 | Having the H-space structure is not a generic property | math.AT | In this note, we answer in negative a question posed by McGibbon about the
generic property of H-space structure.
In fact we verify the conjecture of Roitberg. Incidentally, the same example
also answers in negative the open problem 10 in McGibbon. | math |
398 | Equivariant Phantom maps | math.AT | A successful generalization of phantom map theory to the equivariant case for
all compact Lie groups is obtained in this paper.
One of the key observations is the discovery of the fact that homotopy fiber
of equivariant completion splits as product of equivariant Eilenberg-Maclane
spaces which seems impossible at fir... | math |
399 | Mislin genus of maps | math.AT | In this paper, we prove that the Mislin genus of a (co-)H-map between
(co-)H-spaces under certain natural conditions is a finite abelian group which
generalizes results in Zabrodsky, McGibbon and Hurvitz | math |
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