Splittings and C–complexes

Mj, Mahan; Scott, Peter; Swarup, Gadde

doi:10.2140/agt.2009.9.1971

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Splittings and C–complexes

Mahan Mj, Peter Scott and Gadde Swarup

Algebraic & Geometric Topology 9 (2009) 1971–1986

DOI: 10.2140/agt.2009.9.1971

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

splittings of groups, C–complexes, quasiconvex, codimension one subgroup

Mathematical Subject Classification 2000

Primary: 20F67, 22E40

Secondary: 57M50

References

Publication

Received: 7 August 2009

Revised: 26 August 2009

Accepted: 31 August 2009

Published: 3 October 2009

Authors

Mahan Mj
Department of Mathematics RKM Vivekananda University Belur Math WB-711 202 India

Peter Scott
Mathematics Department University of Michigan Ann Arbor Michigan 48109 USA

Gadde Swarup
718, High Street Road Glen Waverley Victoria 3150 Australia

Volume 9, issue 4 (2009)