Dismantlable classifying space for the family of parabolic subgroups of a relatively hyperbolic group

Abstract

Let $G$ be a group hyperbolic relative to a finite collection of subgroups $\mathcal{P}$. Let $\mathcal{F}$ be the family of subgroups consisting of all the conjugates of subgroups in $\mathcal{P}$, all their subgroups, and all finite subgroups. Then there is a cocompact model for $E_{\mathcal{F}}G$. This result was known in the torsion-free case. In the presence of torsion, a new approach was necessary. Our method is to exploit the notion of dismantlability. A number of sample applications are discussed.

Version accepted for publication in J. Inst. Math. Jussieu

References in corpus (1)

• A note on fine graphs and homological isoperimetric inequalities

Cited by in corpus (3)

• Injectivity results for coarse homology theories
• Bounded cohomology of classifying spaces for families of subgroups
• Relative cohomological dimension of a relatively hyperbolic pair