Quasi-isometric maps and Floyd boundaries of relatively hyperbolic groups.

By V. Gerasimov, L. Potyagailo. 2009

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

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ab23b3d3657b1c99989782c19616a4e1656b770f