English

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

R2 v1 2026-06-21T13:10:07.607Z