Quasi-isometric maps and Floyd boundaries of relatively hyperbolic groups

Original · EN

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 ϕ into a relatively hyperbolic group G is relatively hyperbolic with respect to a system of subgroups whose image under ϕ is situated in a uniformly bounded distance from the parabolic subgroups of G.