The coarse Baum-Connes conjecture for relatively hyperbolic groups (Q2885382)

Let \(G\) be a finitely generated group which is relatively hyperbolic with respect to a finite family of infinite subgroups \(\{G_i\}\) such that for each \(G_i\) the universal space for proper actions can be chosen as a finite \(G_i\)-simplicial complex. The main result of the present paper is that \(G\) fulfills the coarse Baum-Connes conjecture if each \(G_i\) does. The authors also show that \(G\) admits a universal space for proper actions which is a finite \(G\)-simplicial complex. It follows that the Novikov conjecture holds for \(G\) if \(G\) is torsion-free and fulfills the coarse Baum-Connes conjecture.