Volume 9, issue 4 (2009)

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Splittings and C–complexes

Mahan Mj, Peter Scott and Gadde Swarup

Algebraic & Geometric Topology 9 (2009) 1971–1986
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