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The geometry of relative Cayley graphs for subgroups of hyperbolic groups

Ilya Kapovich
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Abstract

We show that if H is a quasiconvex subgroup of a hyperbolic group G then the relative Cayley graph Y (also known as the Schreier coset graph) for G/H is Gromov-hyperbolic. We also observe that in this situation if G is torsion-free and non-elementary and H has infinite index in G then the simple random walk on Y is transient.

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Ilya Kapovich. 2002-01-07. The geometry of relative Cayley graphs for subgroups of hyperbolic groups. https://arxiv.org/abs/math/0201045

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