On Quasiconvexity and Relative Hyperbolic Structures

Abstract

Let G be a group which is hyperbolic relative to a collection of subgroups A, and it is also hyperbolic relative to a collection of subgroups B. Suppose that the collection A contains B. We characterize, for subgroups of G, when quasicovexity relative to A implies quasiconvexity relative to B. We also show that quasiconvexity relative to B implies quasiconvexity relative to A. Some applications are discussed.

Version to appear in Geometriae Dedicata. Included version of Bounded Coset Penetration for general relatively hyperbolic groups, two figures, and updated references

References in corpus (1)

• Separation of Relatively Quasiconvex Subgroups

Cited by in corpus (3)

• Relative hyperbolicity and relative quasiconvexity for countable groups
• Residual finiteness, QCERF, and fillings of hyperbolic groups
• The universal relatively hyperbolic structure on a group and relative quasiconvexity for subgroups