The universal relatively hyperbolic structure on a group and relative quasiconvexity for subgroups

Abstract

We discuss the notion of the universal relatively hyperbolic structure on a group which is used in order to characterize relatively hyperbolic structures on the group. We also study relations between relatively hyperbolic structures on a group and relative quasiconvexity for subgroups of the group.

19 pages, several revisions throughout the paper

References in corpus (5)

• Relative hyperbolicity and relative quasiconvexity for countable groups
• Local Quasiconvexity of Groups acting on Small Cancellation Complexes
• Blowing up and down compacta with geometrically finite convergence actions of a group
• On Quasiconvexity and Relative Hyperbolic Structures
• Hyperbolically embedded virtually free subgroups of relatively hyperbolic groups

Cited by in corpus (4)

• Blowing up and down compacta with geometrically finite convergence actions of a group
• Hyperbolically embedded virtually free subgroups of relatively hyperbolic groups
• On relative hyperbolicity for a group and relative quasiconvexity for a subgroup
• Quasi-Isometries, Boundaries and JSJ-Decompositions of Relatively Hyperbolic Groups