Splittings and C-complexes

Details Splittings and C-complexes Splittings and C-complexes

2009-06-05

arxiv.org/abs/0906.1149v2

Algebraic and Geometric Topology 9 (2009) 1971-1986

Mathematics

Group Theory

v2 final version incorporating referee's comments

Scientific paper

10.2140/agt.2009.9.1971

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.

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