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arXiv · 1602.03941

Acylindrical group actions on quasi-trees

Sahana Balasubramanya
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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 is a (non-elementary) quasi-tree and the action of G on the Cayley graph is acylindrical. Our proof utilizes the notions of hyperbolically embedded subgroups and projection complexes. As a by-product, we obtain some new results about hyperbolically embedded subgroups and quasi-convex subgroups of acylindrically hyperbolic groups.

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Sahana Balasubramanya. 2016-02-12. Acylindrical group actions on quasi-trees. https://doi.org/10.2140/agt.2017.17.2145

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