We study a group which is hyperbolic relative to a finite family of infinite subgroups. We show that the group satisfies the coarse BaumConnes conjecture if each subgroup belonging to the family satisfies the coarse Baum-Connes conjecture and admits a finite universal space for proper actions. If the group is torsion-free, then it satisfies the analytic Novikov conjecture.
- Coarse Baum-Connes conjecture
- Mayer-Vietoris sequence
- relatively hyperbolic group
ASJC Scopus subject areas
- Geometry and Topology