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The Poincaré homology
sphere, lens space surgeries, and some knots with tunnel
number two
Kenneth L. BakerAppendix: Neil R. Hoffman |
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Vol. 305 (2020), No. 1, 1–27
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Abstract |
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We exhibit an infinite family of knots in the Poincaré homology sphere with tunnel number that have a lens space surgery. Notably, these knots are not doubly primitive and provide counterexamples to a few conjectures. Additionally, we update (and correct) our earlier work on Hedden’s almost-simple knots. In the appendix, it is shown that a hyperbolic knot in the Poincaré homology sphere with a lens space surgery has either no symmetries or just a single strong involution. |
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Keywords
Poincaré homology sphere, Dehn surgery, lens space, tunnel
number
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Mathematical Subject Classification 2010
Primary: 57M27
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Milestones
Received: 16 May 2017
Revised: 27 June 2019
Accepted: 2 October 2019
Published: 17 March 2020
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Authors |
| Kenneth L. Baker | |
| Department of Mathematics University of Miami Coral Gables, FL United States |
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| Neil R. Hoffman | |
| Department of Mathematics Oklahoma State University Stillwater, OK United States |
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