Subgroups of relatively hyperbolic groups of Bredon cohomological dimension 2
| Autor: | Eduardo Martínez-Pedroza |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
20F67
20F65 20J05 57S30 57M60 55N25 Pure mathematics Class (set theory) Algebra and Number Theory 010102 general mathematics Geometric Topology (math.GT) Group Theory (math.GR) 0102 computer and information sciences Characterization (mathematics) Cohomological dimension Mathematics::Geometric Topology Mathematics::Algebraic Topology 01 natural sciences Mathematics - Geometric Topology Mathematics::Group Theory Mathematics::K-Theory and Homology 010201 computation theory & mathematics FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Algebraic Topology 0101 mathematics Isoperimetric inequality Algebraic number Mathematics - Group Theory Mathematics |
| Zdroj: | Journal of Group Theory. 20:1031-1060 |
| ISSN: | 1435-4446 1433-5883 |
| DOI: | 10.1515/jgth-2017-0020 |
| Popis: | 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 $FP_2$) 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 $C'(1/6)$ 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. Version accepted for publication in Journal of Group Theory |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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