Michael Puschnigg (Université Aix-Marseille): The Chern-Connes character is not rationally injective
Thursday, 30.06.2011 16:30 im Raum M5
The Chern-Connes character is the unique multiplicative transformation from Kasparov's bivariant K-theory to bivariant local cyclic cohomology.
It provides a link between Kasparov theory, the basic cohomology theory for C*-algebras, and cyclic cohomology, a cohomology theory which is calculable by means of homological algebra.
The Chern-Connes character is a far reaching generalization of the classical Chern character in topological K-theory. In the present talk we show that, contrary to the classical Chern character, the Chern-Connes character is not an isomorphism rationally (it is not even rationally injective).
Counterexamples are provided by the reduced group C*-algebras of suitable discrete groups.