Codimension one subgroups and boundaries of hyperbolic groups
Group Theory
2008-07-21 v1
Abstract
We construct hyperbolic groups with the following properties: The boundary of the group has big dimension, it is separated by a Cantor set and the group does not split. This shows that Bowditch's theorem that characterizes splittings of hyperbolic groups over 2-ended groups in terms of the boundary can not be extended to splittings over more complicated subgroups.
Cite
@article{arxiv.0807.2932,
title = {Codimension one subgroups and boundaries of hyperbolic groups},
author = {Thomas Delzant and Panos Papasoglu},
journal= {arXiv preprint arXiv:0807.2932},
year = {2008}
}