The geometry of relative Cayley graphs for subgroups of hyperbolic groups
Group Theory
2016-09-07 v2
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.
Keywords
Cite
@article{arxiv.math/0201045,
title = {The geometry of relative Cayley graphs for subgroups of hyperbolic groups},
author = {Ilya Kapovich},
journal= {arXiv preprint arXiv:math/0201045},
year = {2016}
}
Comments
14 pages, 7 figures