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arXiv · 1612.03497

Boundaries of Dehn fillings

Daniel Groves·Jason Fox Manning·Alessandro Sisto
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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.

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Daniel Groves, Jason Fox Manning, Alessandro Sisto. 2016-12-11. Boundaries of Dehn fillings. https://doi.org/10.2140/gt.2019.23.2929

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