English

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.

Keywords

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}
}
R2 v1 2026-06-21T11:02:04.398Z