Limit sets of relatively hyperbolic groups

TL;DR

This paper investigates the properties of limit sets in relatively hyperbolic groups, establishing a limit set intersection theorem and exploring dynamical quasiconvexity to generalize results from Kleinian groups.

Contribution

It introduces a limit set intersection theorem for relatively hyperbolic groups and links dynamical quasiconvexity to limit set properties in broader classes of groups.

Findings

Proves a limit set intersection theorem for relatively hyperbolic groups

Establishes dynamical quasiconvexity of undistorted subgroups in groups with Floyd boundary

Generalizes results from Kleinian groups to convergence groups

Abstract

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.