|
|||||
|
|
|
|
|
|
|
|
|
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/ | |
|
