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Limit sets of relatively hyperbolic groups. (English) Zbl 1252.20042
Summary: 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 boundaries.

MSC:
20F67 Hyperbolic groups and nonpositively curved groups
20E07 Subgroup theorems; subgroup growth
30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
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