Relative cohomological dimension of a relatively hyperbolic pair

Abstract

We show that the relative cohomological dimension $\cd(G,H)$ of a relatively hyperbolic pair $(G,H)$ is always finite when $G$ is torsion-free. We also show that this dimension is preserved under quasi-isometries, provided that $G$ is torsion-free and the peripheral subgroup $H$ is unconstricted and of type $F_{\infty }$. As a corollary of our methods, we compute $\cd(G,H)$ in a range of cases.

arXiv commentAccepted version

References in corpus (4)

• Peripheral fillings of relatively hyperbolic groups
• Dismantlable classifying space for the family of parabolic subgroups of a relatively hyperbolic group
• Hyperbolically embedded subgroups and quasi-isometries of pairs
• Finiteness properties and Relatively Hyperbolic Groups