The geometry of relative Cayley graphs for subgroups of hyperbolic groups

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.

14 pages, 7 figures

Cited by in corpus (4)

• The non-amenability of Schreier graphs for infinite index quasiconvex subgroups of hyperbolic groups
• Degree distributions for a class of Circulant graphs
• Enumerations of Cayley graphs
• The generalised word problem for subgroups of hyperbolic groups