Quasi-isometric maps and Floyd boundaries of relatively hyperbolic groups

V. Gerasimov, L. Potyagailo

Published 2009-08-05, updated 2010-12-23Version 8

We describe the kernel of the canonical map from the Floyd boundary of a relatively hyperbolic group to its Bowditch boundary. Using our methods we then prove that a finitely generated group $H$ admitting a quasi-isometric map $\phi$ into a relatively hyperbolic group $G$ is relatively hyperbolic with respect to a system of subgroups whose image under $\phi$ is situated in a uniformly bounded distance from the parabolic subgroups of $G$.