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1,700 | A Comparison of Continuously Controlled and Controlled K-theory | math.KT | We define an unreduced version of the e-controlled lower $K$-theoretic groups
of Ranicki and Yamasaki, and Quinn. We show that the reduced versions of our
groups coincide (in the inverse limit and its first derived, $\lim^1$) with
those of Ranicki and Yamasaki. We also relate the controlled groups to the
continuously c... | math |
1,701 | Cohomology of uniformly powerful p-groups | math.KT | Studies the cohomology of p-central, powerful, p-groups with a certain
extension property. These groups are naturally associated to Lie algebras. The
paper develops a machinery that calculates the first few terms of the Bockstein
spectral sequence in terms of the associated Lie algebras. This is then used to
obtain res... | math |
1,702 | Lifting Lie algebras over the residue field of a discrete valuation ring | math.KT | Studies among other things, the question of whether a Lie algebra over
Z/(p^k)Z lifts to one over Z/(p^(k+1))Z. An obstruction theory is developed and
examples of Fp-Lie algebras which don't lift to Lie algebras over Z/p^2Z are
discussed. An example of an application of the result: A Fp-Lie algebra L with
H^3(L, ad)=0 ... | math |
1,703 | Analytic cyclic cohomology | math.KT | We prove excision in entire and periodic cyclic cohomology and construct a
Chern-Connes character for Fredholm modules over a C*-algebra without
summability restrictions, taking values in a variant of Connes's entire cyclic
cohomology.
Before these results can be obtained, we have to sort out some fundamental
questio... | math |
1,704 | On the K-theory of local fields | math.KT | The authors establish a connection between the Quillen K-theory of certain
local fields and the de Rham-Witt complex of their rings of integers with
logarithmic poles at the maximal ideal. They consider fields K that are
complete discrete valuation fields of characteristic zero with perfect residue
fields k of characte... | math |
1,705 | Infinitesimal K-theory | math.KT | In this paper we study the fiber F of the rational Jones-Goodwillie character
$$ F:=\hofiber(ch:K^\rat(A)@>>>HN^\rat(A)) $$ going from K-theory to negative
cyclic homology of associative rings. We describe this fiber F in terms of
sheaf cohomology. We prove that, for $n\ge 1$, there is an isomorphism: $$
\pi_n(F)\cong ... | math |
1,706 | Cyclic homology of commutative algebras over general ground rings | math.KT | We consider commutative algebras and chain DG algebras over a fixed
commutative ground ring $k$ as in the title. We are concerned with the problem
of computing the cyclic (and Hochschild) homology of such algebras via free
DG-resolutions $\Lambda V @>>> A$. We find spectral sequences
$$E^2_{p,q}=H_p(\Lambda V\otimes\Ga... | math |
1,707 | On the derived functor analogy in the Cuntz-Quillen framework for cyclic homology | math.KT | Cuntz and Quillen have shown that for algebras over a field $k$ with
$char(k)=0$, periodic cyclic homology may be regarded, in some sense, as the
derived functor of (non-commutative) de Rham (co-)homology. The purpose of this
paper is to formalize this derived functor analogy. We show that the
localization ${Def}^{-1}\... | math |
1,708 | On the Leibniz cohomology of vector fields | math.KT | I. M. Gelfand and D. B. Fuks have studied the cohomology of the Lie algebra
of vector fields on a manifold. In this article, we generalize their main tools
to compute the Leibniz cohomology, by extending the two spectral sequences
associated to the diagonal and the order filtration. In particular, we
determine some new... | math |
1,709 | Equivariant K-groups of spheres with actions of involutions | math.KT | We calculate the R(G)-algebra structure on the reduced equivariant K-groups
of two-dimensional spheres on which a compact Lie group G acts as involutions.
In particular, the reduced equivariant K-groups are trivial if G is abelian,
which shows that the previous Y. Yang's calculation in [Yan95] is not true. | math |
1,710 | Equivariant Cyclic Cohomology of H-Algebras | math.KT | We define an equivariant $K_0$-theory for \textit{Yetter-Drinfeld} algebras
over a Hopf algebra with an invertible antipode. We then show that this
definition can be generalized to all Hopf-module algebras. We show that there
exists a pairing, generalizing Connes' pairing, between this theory and a
suitably defined Hop... | math |
1,711 | A New Cyclic Module for Hopf Algebras | math.KT | We define a new cyclic module, dual to the Connes-Moscovici cyclic module,
for Hopf algebras, and give a characteristric map for the coaction of Hopf
algebras. We also compute the resulting cyclic homology for cocommutative Hopf
algebras, and some quantum groups. | math |
1,712 | From Mennicke symbols to Euler class groups | math.KT | Bhatwadekar and Raja Sridharan have constructed a homomorphism of abelian
groups from an orbit set Um(n,A)/E(n,A) of unimodular rows to an Euler class
group. We suggest that this is the last map in a longer exact sequence of
abelian groups. The hypothetical group G that precedes Um(n,A)/E(n,A) in the
sequence is an orb... | math |
1,713 | Hopf Algebra Equivariant Cyclic Homology and Cyclic Homology of Crossed Product Algebras | math.KT | We introduce the cylindrical module $A \natural \mathcal{H}$, where
$\mathcal{H}$ is a Hopf algebra and $A$ is a Hopf module algebra over
$\mathcal{H}$. We show that there exists an isomorphism between
$\mathsf{C}_{\bullet}(A^{op} \rtimes \mathcal{H}^{cop})$ the cyclic module of
the crossed product algebra $A^{op} \rti... | math |
1,714 | A proof of the Baum-Connes conjecture for reductive adelic groups | math.KT | Let F be a global field, A its ring of adeles, G a reductive group over F. We
prove the Baum-Connes conjecture for the adelic group G(A). | math |
1,715 | K-Theory Past and Present | math.KT | A brief account of K-theory written in honour of Friedrich Hirzebruch | math |
1,716 | Para-Hopf algebroids and their cyclic cohomology | math.KT | We introduce the concept of {\it para-Hopf algebroid} and define their cyclic
cohomology in the spirit of Connes-Moscovici cyclic cohomology for Hopf
algebras. Para-Hopf algebroids are closely related to, but different from, Hopf
algebroids. Their definition is motivated by attempting to define a cyclic
cohomology theo... | math |
1,717 | Cyclic Cohomology of Crossed Coproduct Coalgebras | math.KT | We extend our work in~\cite{rm01} to the case of Hopf comodule coalgebras. We
introduce the cocylindrical module $C \natural^{} \mathcal{H}$, where
$\mathcal{H}$ is a Hopf algebra with bijective antipode and $C$ is a Hopf
comodule coalgebra over $\mathcal{H}$. We show that there exists an isomorphism
between the cocycl... | math |
1,718 | Cohomology of trivial extensions of Frobenius algebras | math.KT | We obtain a decomposition for the Hochschild cochain complex of a split
algebra and we study some properties of the cohomology of each term of this
decomposition. Then, we consider the case of trivial extensions, specially of
Frobenius algebras. In particular, we determine completely the cohomology of
the trivial exten... | math |
1,719 | Cyclic Homology of Hopf Comodule Algebras and Hopf Module Coalgebras | math.KT | In this paper we construct a cylindrical module $A \natural \mathcal{H}$ for
an $\mathcal{H}$-comodule algebra $A$, where the antipode of the Hopf algebra
$\mathcal{H}$ is bijective. We show that the cyclic module associated to the
diagonal of $A \natural \mathcal{H}$ is isomorphic with the cyclic module of
the crossed... | math |
1,720 | Hochschild homology and cohomology of generalized Weyl algebras | math.KT | We compute Hochschild homology and cohomology of a class of generalized Weyl
algebras (for short GWA, defined by Bavula in St.Petersbourg Math. Journal 1999
4(1) pp. 71-90). Examples of such algebras are the n-th Weyl algebras, U(sl_2),
primitive quotients of U(sl_2), and subalgebras of invariants of these algebras
und... | math |
1,721 | Algebra structure on the Hochschild cohomology of the ring of invariants of a Weyl algebra under a finite group | math.KT | Let $A_n$ be the $n$-th Weyl algebra, and let
$G\subset\Sp_{2n}(\C)\subset\Aut(A_n)$ be a finite group of linear
automorphisms of $A_n$. In this paper we compute the multiplicative structure
on the Hochschild cohomology $\HH^*(A_n^G)$ of the algebra of invariants of
$G$. We prove that, as a graded algebra, $\HH^*(A_n^G... | math |
1,722 | Homology stability for symplectic groups | math.KT | In this paper the homology stability for symplectic groups over a ring with
finite stable rank is established. First we develop a `nerve theorem' on the
homotopy type of a poset in terms of a cover by subposets, where the cover is
itself indexed by a poset. We use the nerve theorem to show that a poset of
sequences of ... | math |
1,723 | The obstruction to excision in K-theory and in cyclic homology | math.KT | Let $f:A \to B$ be a ring homomorphism of not necessarily unital rings and
$I\triangleleft A$ an ideal which is mapped by f isomorphically to an ideal of
B. The obstruction to excision in K-theory is the failure of the map between
relative K-groups $K_*(A:I) \to K_*(B:f(I))$ to be an isomorphism; it is
measured by the ... | math |
1,724 | Homology stability for unitary groups | math.KT | In this paper homology stability for unitary groups over a ring with finite
unitary stable rank is established. Homology stability of symplectic groups and
orthogonal groups appears as a special case of our results. | math |
1,725 | KK-theory of C*-categories and the analytic assembly map | math.KT | We define KK-theory spectra associated to C*-categories and look at certain
instances of the Kasparov product at this level. This machinery is used to give
a description of the analytic assembly map as a natural map of spectra. | math |
1,726 | Comparisons between periodic, analytic and local cyclic cohomology | math.KT | We compute periodic, analytic and local cyclic cohomology for convolution
algebras of compact Lie groups in order to exhibit differences between these
theories. A surprising result is that the periodic and analytic cyclic
cohomology of the smooth convolution algebras differ, although these algebras
have finite homologi... | math |
1,727 | Unitaire multiplicatif K-moyennable | math.KT | Nous generalisons la theorie de la K-moyennabilite au cas d'un unitaire
multiplicatif regulier V. Nous montrons que si (H,V,U) est un systeme de Kac
K-moyennable, alors pour toute S-algebre A, les algebres $ A\times_{m}\hat S$
(produit croise maximal) et $ A\times \hat S$ (produit croise reduit) sont
KK-equivalentes ou... | math |
1,728 | K-theory of Solvable Groups | math.KT | We first prove that the Whitehead group of a torsion-free virtually solvable
linear group vanishes. Next we make a reduction of the fibered isomorphism
conjecture from virtually solvable groups to a class of virtually solvable
Q-linear groups. Finally we prove an L-theory analogue for elementary amenable
groups. | math |
1,729 | Injective Hopf bimodules, cohomologies of infinite dimensional Hopf algebras and graded-commutativity of the Yoneda product | math.KT | We prove that the category of Hopf bimodules over any Hopf algebra has enough
injectives, which enables us to extend some results on the unification of Hopf
bimodule cohomologies of [T1,T2] to the infinite dimensional case. We also
prove that the cup-product defined on these cohomologies is graded-commutative. | math |
1,730 | Functional equations of higher logarithms | math.KT | We give the first genuine 2-variable functional equation for the
7--logarithm. We investigate and relate identities for the 3-logarithm given by
Goncharov and Wojtkowiak and deduce a certain family of functional equations
for the 4-logarithm. | math |
1,731 | G-Structure on the cohomology of Hopf algebras | math.KT | We prove that Ext^*_A(k,k) is a Gerstenhaber algebra, where A is a Hopf
algebra. In case A=D(H) is the Drinfeld double of a finite dimensional Hopf
algebra H, our results implies the existence of a Gerstenhaber bracket on
H^*_{GS}(H,H). This fact was conjectured by R. Taillefer in math.KT0207154. The
method consists in... | math |
1,732 | K-theory of stratified vector bundles | math.KT | We show that the Atiyah-Hirzebruch K-theory of spaces admits a canonical
generalization for stratified spaces. For this we study algebraic constructions
on stratified vector bundles. In particular the tangent bundle of a stratified
manifold is such a stratified vector bundle. | math |
1,733 | Finite group extensions and the Baum-Connes conjecture | math.KT | In this note, we exhibit a method to prove the Baum-Connes conjecture (with
coefficients) for extensions with finite quotients of certain groups which
already satisfy the Baum-Connes conjecture. Interesting examples to which this
method applies are torsion-free finite extensions of the pure braid groups,
e.g. the full ... | math |
1,734 | Hochschild cohomology of Frobenius algebras | math.KT | Let k be a field and let A be a Frobenius algebra over k. Assume that the
Nakayama automorphism of A associated to a Frobenius homomorphism of A has
finite order m, and k has a m-th primitive root of unity. Then, A has a natural
Z/mZ-gradation. Consider the decomposition of the Hochschild cohomology HH*(A),
of A with c... | math |
1,735 | Higher complex torsion and the framing principle | math.KT | This paper contains a long summary of the basic properties of higher FR
torsion. An attempt is made to simplify the constructions from my book Higher
Franz-Reidemeister Torsion (IP/AMS Studies in Advanced Math 31). Some new basic
theorems are also proved such as the Framing Principle in full generality. This
is used to... | math |
1,736 | Algebraic cobordism | math.KT | Together with F. Morel, we have constructed in \cite{CR, Cobord1, Cobord2} a
theory of {\em algebraic cobordism}, an algebro-geometric version of the
topological theory of complex cobordism. In this paper, we give a survey of the
construction and main results of this theory; in the final section, we propose
a candidate... | math |
1,737 | Norm varieties and algebraic cobordism | math.KT | We outline briefly results and examples related with the bijectivity of the
norm residue homomorphism. We define norm varieties and describe some
constructions. We discuss degree formulas which form a major tool to handle
norm varieties. Finally we formulate Hilbert's 90 for symbols which is the hard
part of the biject... | math |
1,738 | Algebraic K-theory of mapping class groups | math.KT | We prove that the Fibered Isomorphism Conjecture of T. Farrell and L. Jones
holds for various mapping class groups. In many cases, we explicitly calculate
the lower algebraic K-groups, showing that they do not always vanish. | math |
1,739 | Algebra cohomology over a commutative algebra revisited | math.KT | The aim of this paper is to give a relatively easy bicomplex which computes
the Shukla, or Quillen cohomology in the category of associative algebras over
a commutative algebra $A$, in the case when $A$ is an algebra over a field. | math |
1,740 | A characterization of the Dirac Dual Dirac Method | math.KT | Let G be a discrete, torsion free group with a finite dimensional classifying
space BG. We show that the existence of a gamma-element for such G is a metric,
that is, coarse, invariant of G. We also obtain results for groups with
torsion. The method of proof involves showing that a group G possesses a
gamma-element if ... | math |
1,741 | The Baum-Connes Conjecture via Localisation of Categories | math.KT | We redefine the Baum-Connes assembly map using simplicial approximation in
the equivariant Kasparov category. This new interpretation is ideal for
studying functorial properties and gives analogues of the assembly maps for all
equivariant homology theories, not just for the K-theory of the crossed
product. We extend ma... | math |
1,742 | The cyclic homology and K-theory of certain adelic crossed products | math.KT | The multiplicative group of a global field acts on its adele ring by
multiplication. We consider the crossed product algebra of the resulting action
on the space of Schwartz functions on the adele ring and compute its
Hochschild, cyclic and periodic cyclic homology. We also compute the
topological K-theory of the C*-al... | math |
1,743 | Homology stability for Unitary groups II | math.KT | In this note the homology stability problem for hyperbolic unitary groups
over a local ring with an infinite residue field is studied. | math |
1,744 | Third homology of general linear groups | math.KT | The third homology group of GL_n(R) is studied, where R is a `ring with many
units' with center Z(R). The main theorem states that if K_1(Z(R))_Q \simeq
K_1(R)_Q, (e.g. R a commutative ring or a central simple algebra), then
H_3(GL_2(R), Q) --> H_3(GL_3(R), Q) is injective. If R is commutative, Q can be
replaced by a f... | math |
1,745 | The Hochschild cohomology ring modulo nilpotence of a monomial algebra | math.KT | For a finite dimensional monomial algebra $\Lambda$ over a field $K$ we show
that the Hochschild cohomology ring of $\Lambda$ modulo the ideal generated by
homogeneous nilpotent elements is a commutative finitely generated $K$-algebra
of Krull dimension at most one. This was conjectured to be true for any finite
dimens... | math |
1,746 | The Baum-Connes and the Farrell-Jones Conjectures in K- and L-Theory | math.KT | We give a survey of the meaning, status and applications of the Baum-Connes
Conjecture about the topological K-theory of the reduced group C^*-algebra and
the Farrell-Jones Conjecture about the algebraic K- and L-theory of the group
ring of a (discrete) group G. | math |
1,747 | Induction Theorems and Isomorphism Conjectures for K- and L-Theory | math.KT | The Farrell-Jones and the Baum-Connes Conjecture say that one can compute the
algebraic K- and L-theory of the group ring and the topological K-theory of the
reduced group C^*-algebra of a group G in terms of these functors for the
virtually cyclic subgroups or the finite subgroups of G. By induction theory we
want to ... | math |
1,748 | A Controlled Approach to the Isomorphism Conjecture | math.KT | We use a hocolim approach to the Isomorphism Conjecture in K-Theory to
analyze the case of groups of the form $G\rtimes Z$ and $G_1*_{G}G_2$. As an
important corollary we prove that the isomorphism conjecture in K-Theory holds
for a finitely generated free group. | math |
1,749 | The Baum-Connes conjecture, noncommutative Poincare duality and the boundary of the free Group | math.KT | Every hyperbolic group acts continuously on its Gromov boundary. One can form
the corresponding cross-product C*-algebra A. We show that there always exists
a canonical Poincare duality map from the K-theory of A to the K-homology of A.
We show that this map is an isomorphism when the group in question is the free
grou... | math |
1,750 | Twisted $K$-theory | math.KT | Twisted complex $K$-theory can be defined for a space $X$ equipped with a
bundle of complex projective spaces, or, equivalently, with a bundle of
C$^*$-algebras. Up to equivalence, the twisting corresponds to an element of
$H^3(X;\Z)$. We give a systematic account of the definition and basic
properties of the twisted t... | math |
1,751 | Une structure de categorie de modeles de Quillen sur la categorie des dg-categories | math.KT | We construct a cofibrantly generated Quillen model structure on the category
of small differential graded categories.
-----
Nous construisons une structure de categorie de modeles de Quillen a
engendrement cofibrant sur la categorie des petites categories differentielles
graduees. | math |
1,752 | Isomorphism Conjecture for homotopy K-theory and groups acting on trees | math.KT | We discuss an analogon to the Farrell-Jones Conjecture for homotopy algebraic
K-theory. In particular, we prove that if a group G acts on a tree and all
isotropy groups satisfy this conjecture, then G satisfies this conjecture. This
result can be used to get rational injectivity results for the assembly map in
the Farr... | math |
1,753 | Relative cyclic homology of square zero extensions | math.KT | Let k be a characteristic zero field, C a k-algebra and M a square zero two
sided ideal of C. We obtain a new mixed complex, simpler that the canonical
one, giving the Hochschild and cyclic homologies of C relative to M. This
complex resembles the canonical reduced mixed complex of an augmented algebra.
We begin the st... | math |
1,754 | Hochschild duality, localization and smash products | math.KT | In this work we study the class of algebras satisfying a duality property
with respect to Hochschild homology and cohomology, as in [VdB]. More
precisely, we consider the class of algebras $A$ such that there exists an
invertible bimodule $U$ and an integer number $d$ with the property
$H^{\bullet}(A,M)\cong H_{d-\bull... | math |
1,755 | Entire cyclic homology of Schatten ideals | math.KT | Certain cocycles constructed by Connes are characters of $p$-summable
Fredholm modules. In this article, we establish some consequences of the
universal properties which these characters enjoy. Our main technical result is
that the entire cyclic cohomology of the p-th Schatten ideal L^p (respectively,
homology) is inde... | math |
1,756 | The equivariant index theorem in entire cyclic cohomology | math.KT | Let G be a locally compact group acting smoothly and properly by isometries
on a complete Riemannian manifold M, with compact quotient. There is an
assembly map which associates to any G-equivariant K-homology class on M, an
element of the topological K-theory of a suitable Banach completion B of the
convolution algebr... | math |
1,757 | Loday--Quillen--Tsygan Theorem for Coalgebras | math.KT | In this paper we prove that Loday--Quillen--Tsygan Theorem generalizes to the
case of coalgebras. Specifically, we show that the Chevalley--Eilenberg--Lie
homology of the Lie coalgebra of infinite matrices over a coassociative
coalgebra $C$ is generated by the cyclic homology of the underlying coalgebra
$C$ as an exter... | math |
1,758 | Equivariant periodic cyclic homology | math.KT | We define and study equivariant periodic cyclic homology for locally compact
groups. This can be viewed as a noncommutative generalization of equivariant de
Rham cohomology. Although the construction resembles the Cuntz-Quillen approach
to ordinary cyclic homology, a completely new feature in the equivariant
setting is... | math |
1,759 | A new description of equivariant cohomology for totally disconnected groups | math.KT | We consider smooth actions of totally disconnected groups on simplicial
complexes and compare different equivariant cohomology groups associated to
such actions. Our main result is that the bivariant equivariant cohomology
theory introduced by Baum and Schneider can be described using equivariant
periodic cyclic homolo... | math |
1,760 | K- and L-theory of the semi-direct product of the discrete 3-dimensional Heisenberg group by Z/4 | math.KT | We compute the group homology, the topological K-theory of the reduced
C^*-algebra, the algebraic K-theory and the algebraic L-theory of the group
ring of the semi-direct product of the three-dimensional discrete Heisenberg
group by Z/4. These computations will follow from the more general treatment of
a certain class ... | math |
1,761 | Outer authomorphisms and the Jacobian | math.KT | A graphs of rank n (homotopy equivalent to a wedge of n circles) without
``separating edges'' has a canonical n-dimensional compact C^1 manifold
thickening. This implies that the canonical homomorphism f:Out(F_n)-> GL(n,Z)
is trivial in rational cohomology in the stable range answering a question
raised by Hatcher and ... | math |
1,762 | Axioms for higher torsion invariants of smooth bundles | math.KT | We explain the relationship between various characteristic classes for smooth
manifold bundles known as ``higher torsion'' classes. We isolate two
fundamental properties that these cohomology classes may or may not have:
additivity and transfer. We show that higher Franz-Reidemeister torsion and
higher Miller-Morita-Mu... | math |
1,763 | On Compact and Fredholm Operators over C*-algebras and a New Topology in the Space of Compact Operators | math.KT | It is shown that the class of Fredholm operators over an arbitrary unital
$C^{*}$--algebra, which may not admit adjoint ones, can be extended in such a
way that this class of compact operators, used in the definition of the class
of Fredholm operators, contains compact operators both with and without
existence of adjoi... | math |
1,764 | Euler characteristics and Gysin sequences for group actions on boundaries | math.KT | Let G be a locally compact group, let X be a universal proper G-space, and
let Z be a G-equivariant compactification of X that is H-equivariantly
contractible for each compact subgroup H of G. Let W be the resulting boundary.
Assuming the Baum-Connes conjecture for G with coefficients C and C(W), we
construct an exact ... | math |
1,765 | Some Fréchet algebras for which the Chern character is an isomorphism | math.KT | Using similarities between topological $K$-theory and periodic cyclic
homology we show that, after tensoring with $\mathbb C$, for certain Fr\'echet
algebras the Chern character provides an isomorphism between these functors.
This is applied to prove that the Hecke algebra and the Schwartz algebra of a
reductive $p$-ad... | math |
1,766 | The characteristic cohomology class of a triangulated category | math.KT | This is the final version of a series of papers uploaded in May 25, 2005. We
have splitted the long last paper of the previous version in two parts to make
it easier to understand. The results are essentially the same, although the
presentation has changed substantially. The first three papers have not
changed.
This ... | math |
1,767 | Self-stabilization in certain infinite-dimensional matrix algebras | math.KT | Analytical tools to $K$-theory; namely, self-stabilization of rapidly
decreasing matrices, linearization of cyclic loops, and the contractibility of
the pointed stable Toeplitz algebra are discussed in terms of concrete
formulas. Adaptation to the *-algebra and finite perturbation categories is
also considered. Moreove... | math |
1,768 | Correspondences and index | math.KT | We define certain class of correspondences of polarized representations of
$C^*$-algebras. Our correspondences are modeled on the spaces of boundary
values of elliptic operators on bordisms joining two manifolds. In this setup
we define the index. The main subject of the paper is the additivity of the
index. | math |
1,769 | Detecting K-theory by cyclic homology | math.KT | We discuss which part of the rationalized algebraic K-theory of a group ring
is detected via trace maps to Hochschild homology, cyclic homology, periodic
cyclic or negative cyclic homology. | math |
1,770 | Cohomologie des algèbres de Krönecker générales | math.KT | The computation of the Hochschild cohomology $HH^*(T)=H^*(T,T)$ of a
triangular algebra $T=\pmatrix{A&M\cr 0&B\cr}$ was performed in {\bf[BG2]}, by
the means of a certain triangular complex. We use this result here to show how
$HH^*(T)$ splits in little pieces whenever the bimodule $M$ is decomposable. As
an example, w... | math |
1,771 | Coefficients for the Farrell-Jones Conjecture | math.KT | We introduce the Farrell-Jones Conjecture with coefficients in an additive
category with G-action. This is a variant of the Farrell-Jones Conjecture about
the algebraic K- or L-Theory of a group ring RG. It allows to treat twisted
group rings and crossed product rings. The conjecture with coefficients is
stronger than ... | math |
1,772 | Twisted K-theory and cohomology | math.KT | We explore the relations of twisted K-theory to twisted and untwisted
classical cohomology. We construct an Atiyah-Hirzebruch spectral sequence, and
describe its differentials rationally as Massey products. We define the twisted
Chern character. We also discuss power operations in the twisted theory, and
the role of th... | math |
1,773 | Excision in Hopf cyclic homology | math.KT | In this paper we show that both variants of the Hopf cyclic homology has
excision under some natural homological conditions on the objects and the
coefficient module. | math |
1,774 | Comparison morphisms and the Hochschild cohomology ring of truncated quiver algebras | math.KT | A main contribution of this paper is the explicit construction of comparison
morphisms between the standard bar resolution and Bardzell's minimal resolution
for truncated quiver algebras (TQA's).
As a direct application we describe explicitely the Yoneda product and derive
several results on the structure of the coho... | math |
1,775 | Smooth K-theory of locally convex algebras | math.KT | Smooth K-functors are introduced and the smooth K-theory of locally convex
algebras is developed. It is proved that the algebraic and smooth K-functors
are isomorphic on the category of quasi stable real (or complex) Frechet
algebras. | math |
1,776 | Sheaf theory for stacks in manifolds and twisted cohomology for S^1-gerbes | math.KT | This is the first of a series of papers on sheaf theory on smooth and
topological stacks and its applications. The main result of the present paper
is the characterization of the twisted (by a closed integral three-form) de
Rham complex on a manifold. As an object in the derived category it will be
related with the pus... | math |
1,777 | Periodic cyclic homology of Hecke algebras and their Schwartz completions | math.KT | We show that the inclusion of an affine Hecke algebra in its Schwartz
completion induces an isomorphism on periodic cyclic homology. | math |
1,778 | On the K-theory of groups with finite asymptotic dimension | math.KT | It is proved that the assembly maps in algebraic K- and L-theory with respect
to the family of finite subgroups is injective for groups with finite
asymptotic dimension that admit a finite model for the classifying space for
proper actions. The result also applies to certain groups that admit only a
finite dimensional ... | math |
1,779 | The Behavior of Nil-Groups under Localization and the Relative Assembly Map | math.KT | We study the behavior of the Nil-subgroups of K-groups under localization. As
a consequence we obtain that the relative assembly map from the family of
finite subgroups to the family of virtually cyclic subgroups is rationally an
isomorphism. Combined with the equivariant Chern character we obtain a complete
computatio... | math |
1,780 | Homology of SL_n and GL_n over an infinite field | math.KT | The homology of GL_n(F) and SL_n(F) is studied, where F is an infinite field.
Our main theorem states that the natural map H_4(GL_3(F), k) --> H_4(GL_4(F),
k) is injective where k is a field with char(k) \neq 2, 3. For algebraically
closed field F, we prove a better result, namely, H_4(GL_3(F), Z) -->
H_4(GL_4(F), Z) i... | math |
1,781 | Resolutions of free partially commutative monoids | math.KT | A free resolution of free partially commutative monoids is constructed and
with its help the homological dimension of these monoids is calculated. | math |
1,782 | Simplicial homotopy in semi-abelian categories | math.KT | We study Quillen's model category structure for homotopy of simplicial
objects in the context of Janelidze, Marki and Tholen's semi-abelian
categories. This model structure exists as soon as the base category A is
regular Mal'tsev and has enough regular projectives; then the fibrations are
the Kan fibrations of simplic... | math |
1,783 | Third Mac Lane cohomology via categorical rings | math.KT | It is proved that the third Mac Lane cohomology group of a ring R with
coefficients in a bimodule B classifies categorical rings having R as the ring
of isomorphism classes of objects and B as the bimodule of automorphisms of the
neutral object. | math |
1,784 | Equivariant local cyclic homology and the equivariant Chern-Connes character | math.KT | We define and study equivariant analytic and local cyclic homology for smooth
actions of totally disconnected groups on bornological algebras. Our approach
contains equivariant entire cyclic cohomology in the sense of Klimek, Kondracki
and Lesniewski as a special case and provides an equivariant extension of the
local ... | math |
1,785 | Chern character for totally disconnected groups | math.KT | In this paper we construct a bivariant Chern character for the equivariant
KK-theory of a totally disconnected group with values in bivariant equivariant
cohomology in the sense of Baum and Schneider. We prove in particular that the
complexified left hand side of the Baum-Connes conjecture for a totally
disconnected gr... | math |
1,786 | The RO(G)-graded coefficients of (Z/2)^n-equivariant K-theory | math.KT | In this note, we calculate all untwisted and twisted (Z/2)^n-equivariant
K-groups with compact supports of real finite-dimensional linear
representations of (Z/2)^n. The question was motivated by the question of
D-brane charges for orbifold type II string vacua. | math |
1,787 | Algebraic K-theory of Fredholm modules and KK-theory | math.KT | This paper has been withdrawn because it is a duplicate of [math/0609208]. | math |
1,788 | Algebraic K-theory of Fredholm modules and KK-theory | math.KT | Kasparov $KK$-groups $KK(A,B)$ are represented as homotopy groups of the
Pedersen-Weibel nonconnective algebraic $K$-theory spectrum of the additive
category of Fredholm $(A,B)$-bimodules for $A$ and $B$, respectively, a
separable and $\sigma$-unital trivially graded real or complex $C^*$-algebra
acted upon by a fixed ... | math |
1,789 | Inertia and delocalized twisted cohomology | math.KT | We show that the inertia stack of a topological stack is again a topological
stack. We further observe that the inertia stack of an orbispace is again an
orbispace. We show how a U(1)-banded gerbe over an orbispace gives rise to a
flat line bundle over its inertia stack. Via sheaf theory over topological
stacks it give... | math |
1,790 | Modular Lattice for $C_{o}$-Operators | math.KT | We study modularity of the lattice Lat $(T)$ of closed invariant subspaces
for a $C_0$-operator $T$ and find a condition such that Lat $(T)$ is a modular.
Furthermore, we provide a quasiaffinity preserving modularity. | math |
1,791 | On exactness of long sequences of homology semimodules | math.KT | We investigate exactness of long sequences of homology semimodules associated
to Schreier short exact sequences of chain complexes of semimodules. | math |
1,792 | Comparison of spectral sequences involving bifunctors | math.KT | Suppose given functors A x A' -F-> B -G-> C between abelian categories, an
object X in A and an object X' in A' such that certain conditions hold. We show
that, E_1-terms exempt, the Grothendieck spectral sequence of the composition
of F(X,-) and G evaluated at X' is isomorphic to the Grothendieck spectral
sequence of ... | math |
1,793 | On K_1 of a Waldhausen category | math.KT | We give a simple representation of all elements in K_1 of a Waldhausen
category and prove relations between these representatives which hold in K_1. | math |
1,794 | Coarse and equivariant co-assembly maps | math.KT | We study an equivariant co-assembly map that is dual to the usual Baum-Connes
assembly map and closely related to coarse geometry, equivariant Kasparov
theory, and the existence of dual Dirac morphisms. As applications, we prove
the existence of dual Dirac morphisms for groups with suitable
compactifications, that is, ... | math |
1,795 | Cyclic Cohomology and Higher Rank Lattices | math.KT | We give a new proof of the absence of non-trivial idempotents in the group
ring of torsion-free cocompact lattices in SL(n,C). It is based on the
following procedure. We lift the class of the trace in the cyclic cohomology of
the group ring to the crossed product of the smooth functions on the
Furstenberg boundary of S... | math |
1,796 | An analytic index for Lie groupoids | math.KT | For a Lie groupoid there is an analytic index morphism which takes values in
the $K-$theory of the $C^*$-algebra associated to the groupoid. This is a good
invariant but extracting numerical invariants from it, with the existent tools,
is very difficult. In this work, we define another analytic index morphism
associate... | math |
1,797 | Orbifold index and equivariant K-homology | math.KT | We consider a invariant Dirac operator D on a manifold with a proper and
cocompact action of a discrete group G. It gives rise to an equivariant
K-homology class [D]. We show how the index of the induced orbifold Dirac
operator can be calculated from [D] via the assembly map. We further derive a
formula for this index ... | math |
1,798 | Categorical aspects of bivariant K-theory | math.KT | This survey article on bivariant Kasparov theory and E-theory is mainly
intended for readers with a background in homotopical algebra and category
theory. We approach both bivariant K-theories via their universal properties
and equip them with extra structure such as a tensor product and a triangulated
category structu... | math |
1,799 | Homological algebra in bivariant K-theory and other triangulated categories | math.KT | Bivariant (equivariant) K-theory is the standard setting for non-commutative
topology. We may carry over various techniques from homotopy theory and
homological algebra to this setting. Here we do this for some basic notions
from homological algebra: phantom maps, exact chain complexes, projective
resolutions, and deri... | math |
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