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.

arXiv comment25 pages, 3 figures. New added Cor. 1.5 about the existence of closed surface groups in relatively hyperbolic groups

References in corpus (8)

• Relative hyperbolicity and relative quasiconvexity for countable groups
• Separability of double cosets and conjugacy classes in 3-manifold groups
• Some surface subgroups survive surgery
• Separation of Relatively Quasiconvex Subgroups
• A Combination Theorem for Convex Hyperbolic Manifolds, with Applications to Surfaces in 3-Manifolds
• Virtual Amalgamation of Relatively Quasiconvex Subgroups
• A characterization of higher rank symmetric spaces via bounded cohomology
• Geodesics in trees of hyperbolic and relatively hyperbolic groups

Cited by in corpus (2)

• Mixed 3-manifolds are virtually special
• Patterson-Sullivan measures and growth of relatively hyperbolic groups