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

Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata

Published 2011-06-27, updated 2012-05-10Version 3

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.