Chern approximations for generalised group cohomology

Generalised sheaf cohomology theories

This paper is an expanded version of notes for a set of lectures given at the Isaac Newton Institute for Mathematical Sciences during a NATO ASI Workshop entitled “Homotopy Theory of Geometric Categories” on September 23 and 24, 2002. This workshop was part of a program entitled New Contexts in Stable Homotopy Theory that was held at the Institute during the fall of 2002. The intent for the lec...

Chern Character, Hopf Algebras, and Brs Cohomology

We present the construction of a Chern character in cyclic cohomology, involving an arbitrary number of associative algebras in contravariant or covariant position. This is a generalization of the bivariant Chern character for bornological algebras introduced in a previous paper [35], based on Quillen superconnections and heat-kernel regularization. Then we adapt the formalism to the cyclic coh...

Chern classes in Alexander-Spanier cohomology

In this article we construct explicit cocycles in the AlexanderSpanier cohomological complex, representing the Chern character of an element in K-theory

Chern-weil Theory and Equivariant Cohomology

Module cohomology group of inverse semigroup algebras

Let $S$ be an inverse semigroup and let $E$ be its subsemigroup of idempotents. In this paper we define the $n$-th module cohomology group of Banach algebras and show that the first module cohomology group $HH^1_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is zero, for every odd $ninmathbb{N}$. Next, for a Clifford semigroup $S$ we show that $HH^2_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is a Banach sp...