Splittings and C-complexes
Group Theory
2014-11-11 v2 Geometric Topology
Abstract
The intersection pattern of the translates of the limit set of a quasi-convex subgroup of a hyperbolic group can be coded in a natural incidence graph, which suggests connections with the splittings of the ambient group. A similar incidence graph exists for any subgroup of a group. We show that the disconnectedness of this graph for codimension one subgroups leads to splittings. We also reprove some results of Peter Kropholler on splittings of groups over malnormal subgroups and variants of them.
Keywords
Cite
@article{arxiv.0906.1149,
title = {Splittings and C-complexes},
author = {Mahan Mj and Peter Scott and Gadde Swarup},
journal= {arXiv preprint arXiv:0906.1149},
year = {2014}
}
Comments
v2 final version incorporating referee's comments