| Résume | Résumé : Strongly bolic metric spaces are metric spaces whose balls satisfy a condition of smoothness and convexity. In particular, CAT(0) spaces are strongly bolic. The importance of these spaces comes from a theorem of Vincent Lafforgue: let G be a finitely generated group with property (RD); if G admits a proper action on a strongly bolic metric space, then G satisfies the Baum–Connes conjecture. Relative hyperbolicity was defined by Gromov in 1987. It is a generalization of the geometry of hyperbolic groups to a broader class of groups, which includes the fundamental groups of finite-volume hyperbolic manifolds. The rough idea is that a group is hyperbolic relative to a family of subgroups if the geometry of G is hyperbolic outside these subgroups and their translates. In this talk, I will present work in which I construct an action on a strongly bolic space for groups hyperbolic relatively to CAT(0) subgroups. I will in particular describe the proof for hyperbolic groups. |
