Acylindrical group actions on quasi-trees
Group Theory
2018-03-16 v3
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.
Cite
@article{arxiv.1602.03941,
title = {Acylindrical group actions on quasi-trees},
author = {Sahana Balasubramanya},
journal= {arXiv preprint arXiv:1602.03941},
year = {2018}
}