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 general 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 certain
relatively hyperbolic groups. I will in particular describe the case of groups acting on trees.