Proper Group Actions and the Baum-Connes Conjecture (Advanced Courses in Mathematics - CRM Barcelona) by Guido Mislin and Alain Valette
English | ISBN: 3764304081 | 2003 | DJVU | 131 pages | 14,3 mb
This book contains a concise introduction to the techniques used to prove the Baum-Connes conjecture. 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.
The book is aimed at advanced graduate students and researchers in the area, leading to current research problems.

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