Quasi-Isometries, Boundaries and JSJ-Decompositions of Relatively Hyperbolic Groups

Abstract

We demonstrate the quasi-isometry invariance of two important geometric structures for relatively hyperbolic groups: the coned space and the cusped space. As applications, we produce a JSJ-decomposition for relatively hyperbolic groups which is invariant under quasi-isometries and outer automorphisms, as well as a related splitting of the quasi-isometry groups of relatively hyperbolic groups.

Added theorems concerning the structure of QI(G); minor corrections and clarifications; 18 pages, 5 figures

References in corpus (3)

• Relative hyperbolicity and relative quasiconvexity for countable groups
• JSJ decompositions: definitions, existence, uniqueness. II. Compatibility and acylindricity
• The universal relatively hyperbolic structure on a group and relative quasiconvexity for subgroups