Subgroups of relatively hyperbolic groups of Bredon cohomological dimension 2

A remarkable result of Gersten states that the class of hyperbolic groups of cohomological dimension 2 is closed under taking finitely presented (or more generally ) subgroups. We prove the analogous result for relatively hyperbolic groups of Bredon cohomological dimension 2 with respect to the fami...

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Bibliographic Details
Published inJournal of group theory Vol. 20; no. 6; pp. 1031 - 1060
Main Author Martínez-Pedroza, Eduardo
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.11.2017
Walter de Gruyter GmbH
Subjects
Homology
Subgroups
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Summary:A remarkable result of Gersten states that the class of hyperbolic groups of cohomological dimension 2 is closed under taking finitely presented (or more generally ) subgroups. We prove the analogous result for relatively hyperbolic groups of Bredon cohomological dimension 2 with respect to the family of parabolic subgroups. A class of groups where our result applies consists of small cancellation products. The proof relies on an algebraic approach to relative homological Dehn functions, and a characterization of relative hyperbolicity in the framework of finiteness properties over Bredon modules and homological Isoperimetric inequalities.
ISSN:1433-5883
1435-4446
DOI:10.1515/jgth-2017-0020