42 research outputs found
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 -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 -algebras of hyperbolic groups
We construct dense, unconditional subalgebras of the reduced group
-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 -algebras and to delocalized -invariants of
negatively curved manifolds are given