#### 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