Limit sets of relatively hyperbolic groups

Details Limit sets of relatively hyperbolic groups Limit sets of relatively hyperbolic groups

2010-09-08

arxiv.org/abs/1009.1647v3

Mathematics

Group Theory

12 pages. To appear Geometriae Dedicata. With an additional corollary 1.7

Scientific paper

10.1007/s10711-011-9586-z

In this paper, we prove a limit set intersection theorem in relatively hyperbolic groups. Our approach is based on a study of dynamical quasiconvexity of relatively quasiconvex subgroups. Using dynamical quasiconvexity, many well-known results on limit sets of geometrically finite Kleinian groups are derived in general convergence groups. We also establish dynamical quasiconvexity of undistorted subgroups in finitely generated groups with nontrivial Floyd boundary.

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