Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-22T11:52:40.572Z Has data issue: false hasContentIssue false

Classifying Spaces and Boundaries for Relatively Hyperbolic Groups

Published online by Cambridge University Press:  09 June 2003

François Dahmani
Affiliation:
Institut de Recherche Mathématique Avancée, 7 rue René Descartes, 67084 Strasbourg Cedex, France. E-mail: [email protected]
Get access

Abstract

We prove the following: if a group $\Gamma$ is torsion-free, and relatively hyperbolic (with the Bounded Coset Penetration property), relative to a subgroup admitting a finite classifying space, then $\Gamma$ admits a finite classifying space. In this case, if the subgroup admits a boundary in the sense of $\mathcal{Z}$-structures, we prove that $\Gamma$ admits a boundary. This extends classical results of Rips, and of Bestvina and Mess to the relative case.

Type
Research Article
Copyright
2003 London Mathematical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)