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

Part of: Fiber spaces and bundles Special aspects of infinite or finite groups

Published online by Cambridge University Press:  11 April 2017

Eduardo Martínez-Pedroza  and
Piotr Przytycki
Eduardo Martínez-Pedroza
Affiliation:
Memorial University, St. John’s, Newfoundland, Canada A1C 5S7 (emartinezped@mun.ca)
Piotr Przytycki
Affiliation:
McGill University, Montreal, Quebec, Canada H3A 0B9 (piotr.przytycki@mcgill.ca)
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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.

Keywords

20-XX group theory and generalizations57-XX manifolds and cell complexes55-XX algebraic topology

MSC classification

Primary: 20F67: Hyperbolic groups and nonpositively curved groups 55R35: Classifying spaces of groups and $H$-spaces 57S30: Discontinuous groups of transformations

Information

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 18 , Issue 2 , March 2019 , pp. 329 - 345
Copyright
© Cambridge University Press 2017 

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