Proper Group Actions and the Baum-Connes Conjecture (Advanced Courses in Mathematics - CRM Barcelona)
Edition: 1 edition
Publisher: Birkhäuser Basel
Published: September 17, 2003
Language: eng
Format: Paperback
Number of pages: 131
ISBN-13: 9783764304089
Subjects: Differential & Riemannian geometry; Algebra - General; Group Theory; Mathematics; Science/Mathematics; Geometry - General; Geometry - Algebraic; Algebraic Topology; Mathematics / Topology
First sentence: The Baum-Connes Conjecture predicts that the K-theory of the reduced C*-algebra C(G) of a group G can be computed as the KG-homology of the so-called universal space for proper G-actions, EG.
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.