The Baum-Connes assembly map and the generalized Bass conjecture

Details The Baum-Connes assembly map and the generalized Bass conjecture The Baum-Connes assembly map and the generalized Bass conjecture

2007-07-25

arxiv.org/abs/0707.3655v1

Mathematics

K-Theory and Homology

5 pages

Scientific paper

We show that the image of Connes-Karoubi-Chern character, restricted to the image of the Baum-Connes assembly map in the Bott-periodized topological K-theory of the complex group algebra, lies in the elliptic summand of the (periodic) cyclic homology of the group algebra. This implies that for any (weighted) ell-1 completion of the group algebra, rational surjectivity of the Baum-Connes assembly map implies the generalized Bass conjecture for that algebra.

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