Bivariant \(K\)-theory for Banach algebras and the Baum-Connes conjecture. (\(K\)-théorie bivariante pour les algèbres de Banach et conjecture de Baum-Connes.) (French) Zbl 1084.19003

Lafforgue, Vincent

Invent. Math. 149, No. 1, 1-95 (2002).

Summary: Cette introduction est composée de trois parties: un exposé historique, l’explication de l’idée principale de l’article et la description des applications à la conjecture de Baum-Connes.

MSC:

19K35	Kasparov theory (\(KK\)-theory)
46L80	\(K\)-theory and operator algebras (including cyclic theory)
58J22	Exotic index theories on manifolds
46M20	Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)
46H25	Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)