Height in Splitting of Relatively Hyperbolic Groups

Abstract

Given a finite graph of relatively hyperbolic groups with its fundamental group relatively hyperbolic and edge groups quasi-isometrically embedded and relatively quasiconvex in vertex groups, we prove that vertex groups are relatively quasiconvex if and only if all the vertex groups have finite relative height in the fundamental group.

Minor errors corrected, accepted in Geom. Dedicata

References in corpus (4)

• Relative hyperbolicity and relative quasiconvexity for countable groups
• Packing subgroups in relatively hyperbolic groups
• Relative Hyperbolicity, Trees of Spaces and Cannon-Thurston Maps
• A Combination Theorem for Strong Relative Hyperbolicity