English

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