Boundaries of Dehn fillings

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.

v2: 52 pages, 2 figures. Moved some technical material to an appendix. Added outline and Theorem 4.8 about free product structure

Cited by in corpus (4)

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• Relative cubulations and groups with a 2-sphere boundary
• Cohomology of group theoretic Dehn fillings I: Cohen-Lyndon type theorems
• A spectral sequence for Dehn fillings