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Finite surgeries on three-tangle pretzel knots
David Futer, Masaharu Ishikawa, Yuichi Kabaya, Thomas W Mattman and Koya Shimokawa |
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Algebraic & Geometric Topology 9 (2009) 743–771 |
Abstract |
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We classify Dehn surgeries on (p,q,r) pretzel knots that result in a manifold of finite fundamental group. The only hyperbolic pretzel knots that admit nontrivial finite surgeries are (−2,3,7) and (−2,3,9). Agol and Lackenby’s 6–theorem reduces the argument to knots with small indices p,q,r. We treat these using the Culler–Shalen norm of the SL(2, C)–character variety. In particular, we introduce new techniques for demonstrating that boundary slopes are detected by the character variety. |
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Dedicated to Professor Akio Kawauchi on the occasion of his 60th birthday. |
Keywordspretzel knot, exceptional Dehn surgery, finite surgery, Culler–Shalen seminorm |
Mathematical Subject ClassificationPrimary: 57M05, 57M25, 57M50 |
References |
PublicationReceived: 29 September 2008 |
Authors |
| David Futer | |
| Mathematics Department Temple University Philadelphia, PA 19122 USA |
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| Masaharu Ishikawa | |
| Mathematical Institute Tohoku University Sendai, 980-8578 Japan |
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| Yuichi Kabaya | |
| Department of Mathematics Tokyo Institute of Technology 2-12-1 Oh-okayama, Meguro-ku Tokyo 152-8551 Japan |
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| Thomas W Mattman | |
| Department of Mathematics and
Statistics California State University at Chico Chico, CA 95929-0525 USA |
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| Koya Shimokawa | |
| Department of Mathematics Saitama University Saitama 338-8570 Japan |
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