Proper Group Actions and the Baum-Connes Conjectur

Proper Group Actions and the Baum-Connes Conjecture
131 pages | Sep 22 2004 |ISBN: 3764304081 | PDF | 5.5 Mb
The Baum-Connes conjecture predicts that the K-homology of the reduced C^*-algebra of a group can be computed as the equivariant K-homology of the classifying space for proper actions. The approach is expository, but it contains proofs of many basic results on topological K-homology and the K-theory of C^*-algebras. It features a detailed introduction to Bredon homology for infinite groups, with applications to K-homology. It also contains a detailed discussion of naturality questions concerning the assembly map, a topic not well documented in the literature.