Geometry and Topology Seminar
A combination theorem for subgroups
of relatively hyperbolic groups
Eduardo Martinez, University of Oklahoma
Details
Wednesday February 7, 2007
809 Physical Sciences Center
3:45 pm
Abstract
The class of relatively hyperbolic groups was introduced by M. Gromov, and has been intensively study after works of B. Farb and B.H. Bowditch in the late 90's. This class of geometric groups includes, for instance, the class of fundamental groups of finite volume hyperbolic manifolds. Recently, D. Osin introduced the notion of relatively quasi-convex subgroup of a relatively hyperbolic group as a generalization of the notion of quasi-convex subgroup in a hyperbolic group. An example of a relatively quasi-convex subgroup is the subgroup induced by a convex surface embedded in a hyperbolic 3-manifold. In this talk, a combination theorem for quasi-convex subgroups of relatively hyperbolic groups will be presented. This result has the flavor of the Klein-Maskit combination theorems and generalizes results by Rita Gitik.