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Finite surgeries on three-tangle pretzel knots
Futer, D Ishikawa, M Kabaya, Y Mattman, TW Shimokawa, K
Futer, D
Ishikawa, M
Kabaya, Y
Mattman, TW
Shimokawa, K
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Journal Article
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2009-12-01
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10.2140/agt.2009.9.743
Abstract
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. © 2009 Mathematical Sciences Publishers.
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Mathematical Sciences Publishers
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Algebraic and Geometric Topology
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