Relative Quasiconvexity using Fine Hyperbolic Graphs

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.

21 pages, 6 figures. New section on fine graphs. Version to appear in AGT

References in corpus (3)

• Relative hyperbolicity and relative quasiconvexity for countable groups
• Combination of quasiconvex subgroups of relatively hyperbolic groups
• Separation of Relatively Quasiconvex Subgroups

Cited by in corpus (3)

• Lifting Group Actions, Equivariant Towers and Subgroups of Non-positively Curved Groups
• A note on fine graphs and homological isoperimetric inequalities
• Dismantlable classifying space for the family of parabolic subgroups of a relatively hyperbolic group