The coarse Baum-Connes conjecture for relatively hyperbolic groups

Abstract

We study a group which is hyperbolic relative to a finite family of infinite subgroups. We show that the group satisfies the coarse Baum-Connes conjecture if each subgroup belonging to the family satisfies the coarse Baum-Connes conjecture and admits a finite universal space for proper actions. Especially, the group satisfies the analytic Novikov conjecture.

17 pages

References in corpus (1)

• Relative hyperbolicity and relative quasiconvexity for countable groups

Cited by in corpus (7)

• A coarse Cartan-Hadamard theorem with application to the coarse Baum-Connes conjecture
• Coronae of product spaces and the Coarse Baum-Connes conjecture
• The equivariant coarse Novikov conjecture and coarse embedding
• Helly groups, coarsely Helly groups, and relative hyperbolicity
• Coronae of relatively hyperbolic groups and coarse cohomologies
• Extending Properties to Relatively Hyperbolic Groups
• $L^p$ coarse Baum-Connes conjecture via $C_0$ coarse geometry