Bivariant K-theory for Banach algebras, groupoids and Baum-Connes conjectures. With an appendix by Herve Oyono-Oyono

摘要

We construct a KK-theory for Banach algebras, equivariant with respect to the action of a groupoid. We prove the Baum-Connes conjecture with commutative coefficients for hyperbolic groups and for the Poincare groupoids of foliations with a compact base and a longitudinal Riemannian metrics with negative sectional curvature.