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.

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Keywords
relative ends, Schreier graphs, hyperbolic groups, Bestvina–Mess condition
Primary: 20F65
Secondary: 20F10