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2017 Acylindrical group actions on quasi-trees
Sahana Balasubramanya
Algebr. Geom. Topol. 17(4): 2145-2176 (2017). DOI: 10.2140/agt.2017.17.2145

Abstract

A group G is acylindrically hyperbolic if it admits a non-elementary acylindrical action on a hyperbolic space. We prove that every acylindrically hyperbolic group G has a generating set X such that the corresponding Cayley graph Γ is a (non-elementary) quasi-tree and the action of G on Γ is acylindrical. Our proof utilizes the notions of hyperbolically embedded subgroups and projection complexes. As an application, we obtain some new results about hyperbolically embedded subgroups and quasi-convex subgroups of acylindrically hyperbolic groups.

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Sahana Balasubramanya. "Acylindrical group actions on quasi-trees." Algebr. Geom. Topol. 17 (4) 2145 - 2176, 2017. https://doi.org/10.2140/agt.2017.17.2145

Information

Received: 4 March 2016; Revised: 19 October 2016; Accepted: 30 October 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06762688
MathSciNet: MR3685605
Digital Object Identifier: 10.2140/agt.2017.17.2145

Subjects:
Primary: 20F67
Secondary: 20E08, 20F65

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 4 • 2017
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