The Chern-Connes character is not rationally injective

We show that the Chern-Connes character from Kasparov's bivariant K-theory to bivariant local cyclic cohomology is not always rationally injective. Counterexamples are provided by the reduced group $C^*$-algebras of word-hyperbolic groups with Kazhdan's property (T). The proof makes essential use of Skandalis' work on K-nuclearity and of Lafforgue's recent demonstration of the Baum-Connes conjecture with coefficients for word-hyperbolic groups

Local cyclic homology of group Banach algebras of "non-positively curved" discrete groups

We calculate the local cyclic homology of group Banach-algebras of discrete groups acting properly, isometrically and cocompactly on a CAT(0)-space.Comment: 33 page

New holomorphically closed subalgebras of C∗C^*-algebras of hyperbolic groups

We construct dense, unconditional subalgebras of the reduced group $C^*$-algebra of a word-hyperbolic group, which are closed under holomorphic functional calculus and possess many bounded traces. Applications to the cyclic cohomology of group $C^*$-algebras and to delocalized $L^2$-invariants of negatively curved manifolds are given

Excision in cyclic homology theories

International audienc

A survey of asymptotic cyclic cohomology

International audienc