Dehn fillings and elementary splittings

TL;DR

This paper investigates how specific splitting properties of relatively hyperbolic groups and their boundary connectivity are preserved under long Dehn fillings, providing insights into the structural stability of these groups.

Contribution

It establishes conditions under which non-splitting properties and boundary connectivity are maintained during long Dehn fillings of relatively hyperbolic groups.

Findings

Splitting properties are preserved under long Dehn fillings.

Connectivity of the Bowditch boundary persists in long fillings.

Certain structural features of relatively hyperbolic groups remain stable during fillings.

Abstract

We consider conditions on relatively hyperbolic groups about the non-existence of certain kinds of splittings, and show these properties persist in long Dehn fillings. We deduce that certain connectivity properties of the Bowditch boundary persist under long fillings.