Volume 23, issue 6 (2019)

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Boundaries of Dehn fillings

Daniel Groves, Jason Fox Manning and Alessandro Sisto

Geometry & Topology 23 (2019) 2929–3002
Abstract

We begin an investigation into the behavior of Bowditch and Gromov boundaries under the operation of Dehn filling. In particular, we show many Dehn fillings of a toral relatively hyperbolic group with $2$–sphere boundary are hyperbolic with $2$–sphere boundary. As an application, we show that the Cannon conjecture implies a relatively hyperbolic version of the Cannon conjecture.

Keywords
relatively hyperbolic groups, boundaries, Dehn filling
Primary: 20F67
Secondary: 57M07