Connectedness of Bowditch Boundary of Dehn Fillings

TL;DR

This paper investigates how the connectedness of the Bowditch boundary of relatively hyperbolic groups is preserved under long Dehn fillings, removing previous restrictions on peripheral subgroups.

Contribution

It demonstrates that the connectedness of the Bowditch boundary persists in long Dehn fillings without requiring peripheral subgroups to be virtually polycyclic.

Findings

Connectedness of Bowditch boundary is preserved in sufficiently long Dehn fillings.

Removal of the restriction on peripheral subgroups being virtually polycyclic.

Provides new insights into the boundary behavior under Dehn fillings.

Abstract

We study Dehn fillings of relatively hyperbolic group pairs $(\Gamma, \P)$ and the persistence of connectedness of Bowditch boundary in sufficiently long Dehn fillings. We show that the restriction of peripheral subgroups to virtually polycyclic subgroups is not needed.