#### Volume 18, issue 5 (2018)

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Ends of Schreier graphs of hyperbolic groups

### Audrey Vonseel

Algebraic & Geometric Topology 18 (2018) 3089–3118
##### Abstract

We study the number of ends of a Schreier graph of a hyperbolic group. Let $G$ be a hyperbolic group and let $H$ be a subgroup of $G\phantom{\rule{0.3em}{0ex}}$. In general, there is no algorithm to compute the number of ends of a Schreier graph of the pair $\left(G,H\right)$. However, assuming that $H$ is a quasiconvex subgroup of $G\phantom{\rule{0.3em}{0ex}}$, we construct an algorithm.

##### Keywords
relative ends, Schreier graphs, hyperbolic groups, Bestvina–Mess condition
Primary: 20F65
Secondary: 20F10
##### Publication
Received: 14 February 2018
Revised: 11 June 2018
Accepted: 21 June 2018
Published: 22 August 2018
##### Authors
 Audrey Vonseel Institut de Recherche Mathématique Avancée Université de Strasbourg, CNRS, UMR 7501 Strasbourg France