Algebraic & Geometric Topology 11 (2011) 477–501

DOI: 10.2140/agt.2011.11.477

Abstract

We provide a new and elegant approach to relative quasiconvexity for relatively hyperbolic groups in the context of Bowditch’s approach to relative hyperbolicity using cocompact actions on fine hyperbolic graphs. Our approach to quasiconvexity generalizes the other definitions in the literature that apply only for countable relatively hyperbolic groups. We also provide an elementary and self-contained proof that relatively quasiconvex subgroups are relatively hyperbolic.

Keywords

hyperbolic group, quasiconvex subgroup, fine graph, relatively hyperbolic group

Mathematical Subject Classification

Primary: 20F06, 20F65, 20F67

References

Publication

Received: 10 September 2010
Revised: 6 November 2010
Accepted: 18 November 2010
Published: 30 January 2011

Authors