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DISMANTLABLE CLASSIFYING SPACE FOR THE FAMILY OF PARABOLIC SUBGROUPS OF A RELATIVELY HYPERBOLIC GROUP

  • Eduardo Martínez-Pedroza (a1) and Piotr Przytycki (a2)

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.

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