The Chern-Connes character is not rationally injective
K-Theory and Homology
2011-04-13 v2
Abstract
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.
Cite
@article{arxiv.1102.5262,
title = {The Chern-Connes character is not rationally injective},
author = {Michael Puschnigg},
journal= {arXiv preprint arXiv:1102.5262},
year = {2011}
}