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Boundaries of Dehn
fillings
Daniel Groves, Jason Fox Manning and Alessandro Sisto |
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Geometry & Topology 23 (2019) 2929–3002
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Abstract |
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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 –sphere boundary are hyperbolic with –sphere boundary. As an application, we show that the Cannon conjecture implies a relatively hyperbolic version of the Cannon conjecture. |
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Keywords
relatively hyperbolic groups, boundaries, Dehn filling
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Mathematical Subject Classification 2010
Primary: 20F67
Secondary: 57M07
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References |
Publication
Received: 19 December 2017
Revised: 22 October 2018
Accepted: 8 January 2019
Published: 1 December 2019
Proposed: Ian Agol
Seconded: Benson Farb, Bruce Kleiner
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Authors |
| Daniel Groves | |
| Department of Mathematics,
Statistics and Computer Science University of Illinois at Chicago Chicago, IL United States |
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| Jason Fox Manning | |
| Department of Mathematics Cornell University Ithaca, NY United States |
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| Alessandro Sisto | |
| Department of Mathematics ETH Zürich Zürich Switzerland |
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