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

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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relatively hyperbolic groups, boundaries, Dehn filling
Mathematical Subject Classification 2010
Primary: 20F67
Secondary: 57M07
Received: 19 December 2017
Revised: 22 October 2018
Accepted: 8 January 2019
Published: 1 December 2019
Proposed: Ian Agol
Seconded: Benson Farb, Bruce Kleiner
Daniel Groves
Department of Mathematics, Statistics and Computer Science
University of Illinois at Chicago
Chicago, IL
United States
Jason Fox Manning
Department of Mathematics
Cornell University
Ithaca, NY
United States
Alessandro Sisto
Department of Mathematics
ETH Zürich