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The prism manifold
realization problem
William Ballinger, Chloe Ching-Yun Hsu, Wyatt Mackey, Yi Ni, Tynan Ochse and Faramarz Vafaee |
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Algebraic & Geometric Topology 20 (2020) 757–816
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Abstract |
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The spherical manifold realization problem asks which spherical three-manifolds arise from surgeries on knots in . In recent years, the realization problem for C–, T–, O– and I–type spherical manifolds has been solved, leaving the D–type manifolds (also known as the prism manifolds) as the only remaining case. Every prism manifold can be parametrized as for a pair of relatively prime integers and . We determine a list of prism manifolds that can possibly be realized by positive integral surgeries on knots in when . Based on the forthcoming work of Berge and Kang, we are confident that this list is complete. The methodology undertaken to obtain the classification is similar to that of Greene for lens spaces. |
Keywords
prism manifold, Dehn surgery, changemaker
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Mathematical Subject Classification 2010
Primary: 57M25, 57R65
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References |
Publication
Received: 17 May 2018
Revised: 6 June 2019
Accepted: 24 June 2019
Published: 23 April 2020
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Authors |
| William Ballinger | |
| Department of Mathematics Princeton University Princeton, NJ United States |
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| Chloe Ching-Yun Hsu | |
| Department of Mathematics California Institute of Technology Pasadena, CA United States |
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| Wyatt Mackey | |
| Department of Mathematics Stanford University Stanford, CA United States |
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| Yi Ni | |
| Department of Mathematics California Institute of Technology Pasadena, CA United States |
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| Tynan Ochse | |
| Department of Mathematics University of Texas, Austin Austin, TX United States |
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| Faramarz Vafaee | |
| Department of Mathematics Duke University Durham, NC United States |
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