Combination of fully quasiconvex subgroups and its applications

Abstract

In this paper, we state two combination theorems for relatively quasiconvex subgroups in a relatively hyperbolic group. Applications are given to the separability of double cosets of certain relatively quasiconvex subgroups and the existence of closed surface subgroups in relatively hyperbolic groups.

25 pages, 3 figures. New added Cor. 1.5 about the existence of closed surface groups in relatively hyperbolic groups

References in corpus (2)

• A characterization of higher rank symmetric spaces via bounded cohomology
• Geodesics in trees of hyperbolic and relatively hyperbolic groups