Hyperbolic groups with homeomorphic Gromov boundaries
Group Theory
2013-03-28 v1 Geometric Topology
Abstract
We show that the Gromov boundary of the free product of two infinite hyperbolic groups is uniquely determined up to homeomorphism by the homeomorphism types of the boundaries of its factors. We generalize this result to graphs of hyperbolic groups over finite subgroups. Finally, we give a necessary and sufficient condition for the Gromov boundaries of any two hyperbolic groups to be homeomorphic (in terms of the topology of the boundaries of factors in terminal splittings over finite subgroups).
Cite
@article{arxiv.1303.6774,
title = {Hyperbolic groups with homeomorphic Gromov boundaries},
author = {A. Martin and J. Swiatkowski},
journal= {arXiv preprint arXiv:1303.6774},
year = {2013}
}
Comments
15 pages