Proper Group Actions and the Baum-Connes Conjecture (Advanced Courses in Mathematics - CRM Barcelona)

Description:

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.

subjects: Group theory,  Operator algebras,  KK-theory,  Baum-Connes conjecture,  Mathematics,  Geometry, algebraic,  Topological Groups,  Algebraic topology