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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
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Abstract |
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We classify Dehn surgeries on pretzel knots that result in a manifold of finite fundamental group. The only hyperbolic pretzel knots that admit nontrivial finite surgeries are and . Agol and Lackenby’s –theorem reduces the argument to knots with small indices . We treat these using the Culler–Shalen norm of the –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. |
Keywords
pretzel knot, exceptional Dehn surgery, finite surgery,
Culler–Shalen seminorm
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Mathematical Subject Classification 2000
Primary: 57M05, 57M25, 57M50
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References |
Publication
Received: 29 September 2008
Accepted: 10 February 2009
Published: 20 April 2009
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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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