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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]
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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

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