Proper Group Actions and the Baum-Connes Conjecture

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.

List of contents

Equivariant K-Homology of the Classifying Space for Proper Actions.- On the Baum-Connes Assembly Map for Discrete Groups.

Summary

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.

Product details

• Authors: G. Mislin, Guid Mislin, Guido Mislin, A. Valette, Alain Valette
• Publisher: Springer, Basel
• Languages: English
• Product format: Paperback / Softback
• Released: 30.09.2003
• EAN: 9783764304089
• ISBN: 978-3-7643-0408-9
• No. of pages: 140
• Weight: 270 g
• Illustrations: 131 p. 2 illus.
• Series: Advanced Courses in Mathematics - CRM Barcelona; Advanced Courses in Mathematics CRM Barcelona; Advanced Courses in Mathematics - CRM Barcelona
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; B, Mathematics and Statistics, Algebraic Geometry, Topological Groups, Lie Groups, Topological groups, Lie groups, Topological Groups and Lie Groups, Groups & group theory, Algebraic Topology, Algebraic topology;Grad;K-theory;group theory;homology