The geometry of relative Cayley graphs for subgroups of hyperbolic groups

Details The geometry of relative Cayley graphs for subgroups of hyperbolic groups The geometry of relative Cayley graphs for subgroups of hyperbolic groups

2002-01-07

arxiv.org/abs/math/0201045v2

Mathematics

Group Theory

14 pages, 7 figures

Scientific paper

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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