Volume 11, issue 1 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Relative quasiconvexity using fine hyperbolic graphs

Eduardo Martínez-Pedroza and Daniel T Wise

Algebraic & Geometric Topology 11 (2011) 477–501
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 2000
Primary: 20F06, 20F65, 20F67
References
Publication
Received: 10 September 2010
Revised: 6 November 2010
Accepted: 18 November 2010
Published: 30 January 2011
Authors
Eduardo Martínez-Pedroza
Department of Mathematics and Statistics
McMaster University
1280 Main Street West
Hamilton ON L8S 4K1
Canada
http://www.math.mcmaster.ca/~emartine
Daniel T Wise
Department of Mathematics & Statistics
McGill University
Burnside Hall
805 Sherbrooke Street West
Montreal QC H3A 2K6
Canada
http://www.math.mcgill.ca/wise/