English
Related papers

Related papers: Chern Classes in Alexander-Spanier Cohomology

200 papers

Given a C$^*$-dynamical system $(A, G, \alpha)$ one defines a homomorphism, called the Chern-Connes character, that take an element in $K_0(A) \oplus K_1(A)$, the K-theory groups of the C$^*$-algebra $A$, and maps it into…

Operator Algebras · Mathematics 2008-08-06 David P. Dias

In the paper [Ba-Be-Mdz], using the Alexander-Spanier cochains based on the normal coverings, the exact homology theory $\bar{H}^N_*(-,-;G)$, the so called Alexander-Spanier homology theory, is defined. In the paper we will use the method…

Algebraic Topology · Mathematics 2024-03-25 Anzor Beridze

In this paper we compute the K-theory (algebraic and topological) and entire periodic cyclic homology for compact quantum groups, define Chern characters between them and show that the Chern characters in both topological and algebraic…

Quantum Algebra · Mathematics 2014-06-09 Do Ngoc Diep , Aderemi O. Kuku , Nguyen Quoc Tho

We show that the bivariant Chern character in entire cyclic cohomology constructed in a previous paper in terms of superconnections and heat kernel regularization, retracts on periodic cocycles under some finite summability conditions. The…

Mathematical Physics · Physics 2007-05-23 Denis Perrot

We construct for an equivariant cohomology theory for proper equivariant CW-complexes an equivariant Chern character, provided that certain conditions about the coefficients are satisfied. These conditions are fulfilled if the coefficients…

Geometric Topology · Mathematics 2007-05-23 Wolfgang Lueck

We provide a formula for the Chern character of a holomorphic vector bundle in the hyper-cohomology of the de Rham complex of holomorphic sheaves on a complex manifold. This Chern character can be thought of as a completion of the Chern…

Algebraic Geometry · Mathematics 2025-04-11 Cheyne Glass , Thomas Tradler , Mahmoud Zeinalian

Given a smooth action of a Lie group on a manifold, we give two constructions of the Chern character of an equivariant vector bundle in the cyclic cohomology of the crossed product algebra. The first construction associates a cycle to the…

Differential Geometry · Mathematics 2023-04-10 Bjarne Kosmeijer , Hessel Posthuma

A cocycle $\Omega: P \times G \to H$ taking values in a Lie group $H$ for a free right action of $G$ on $P$ defines a principal bundle $Q$ with the structure group $H$ over $P/G.$ The Chern character of a vector bundle associated to $Q$…

Differential Geometry · Mathematics 2012-05-11 Jouko Mickelsson

The purpose of this work is to provide details about the construction of the Chern character for categorical sheaves mentioned in our previous work "Chern character, loop spaces and derived algebraic geometry". For this, we introduce and…

Algebraic Geometry · Mathematics 2011-02-15 B. Toen , G. Vezzosi

We introduce and study elementary properties of graph homology of algebras. This new homology theory shares many features of cyclic and Hochschild homology. We also define a graph K-theory together with an analog of Chern character.

K-Theory and Homology · Mathematics 2007-05-23 M. V. Movshev

We examine Hopf cyclic cohomology in the same context as the analysis of the geometry of loop spaces $LX$ in derived algebraic geometry and the resulting close relationship between $S^1$-equivariant quasi-coherent sheaves on $LX$ and…

K-Theory and Homology · Mathematics 2019-04-09 Ilya Shapiro

We construct a model of differential K-theory, using the geometrically defined Chern forms, whose cocycles are certain equivalence classes of maps into the Grassmannians and unitary groups. In particular, we produce the circle-integration…

K-Theory and Homology · Mathematics 2015-07-08 Thomas Tradler , Scott O. Wilson , Mahmoud Zeinalian

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.…

K-Theory and Homology · Mathematics 2007-05-23 Ralf Meyer

We introduce Chern classes in $U(m)$-equivariant homotopical bordism that refine the Conner-Floyd-Chern classes in the $MU$-cohomology of $B U(m)$. For products of unitary groups, our Chern classes form regular sequences that generate the…

Algebraic Topology · Mathematics 2024-01-08 Stefan Schwede

In this paper, we construct Chern classes from the relative $K$-theory of modulus pairs to the relative motivic cohomology defined by Binda-Saito. An application to relative motivic cohomology of henselian dvr is given.

K-Theory and Homology · Mathematics 2019-11-15 Ryomei Iwasa , Wataru Kai

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…

K-Theory and Homology · Mathematics 2008-09-29 Maarten Solleveld

These notes form the next episode in a series of articles dedicated to a detailed proof of a cohomological index formula for transversally elliptic pseudo-differential operators and applications. The first two chapters are already available…

Differential Geometry · Mathematics 2008-01-21 Paul-Emile Paradan , Michèle Vergne

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…

K-Theory and Homology · Mathematics 2007-05-23 Michael Atiyah , Graeme Segal

We construct a quasi-inverse of the cochain map on the negative cyclic complexes of the second kind induced from the quasi-Yoneda embedding on a curved dg algebra. This gives an explicit formula for the Chern character of a perfect module.

Algebraic Geometry · Mathematics 2022-02-24 Kuerak Chung , Bumsig Kim , Taejung Kim

Given a matrix factorization, we use the Atiyah class to give an algebraic Chern-Weil type construction to its Chern character; this allows us to realize the Chern character in an explicit way. It also generalizes the existing result to any…

Rings and Algebras · Mathematics 2013-10-29 Xuan Yu