Quasi-isometric maps and Floyd boundaries of relatively hyperbolic groups

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

2009-08-05

arxiv.org/abs/0908.0705v8

Mathematics

Group Theory

17 pages, 1 figure

Scientific paper

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 $G$.

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