Finite surgeries on three-tangle pretzel knots

D. Futer; M. Ishikawa; Y. Kabaya; T. Mattman; K. Shimokawa

doi:10.2140/agt.2009.9.743

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arXiv · 0809.4278

Finite surgeries on three-tangle pretzel knots

D. Futer·M. Ishikawa·Y. Kabaya·T. Mattman·K. Shimokawa

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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 non-trivial 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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D. Futer, M. Ishikawa, Y. Kabaya, T. Mattman, K. Shimokawa. 2009-03-27. Finite surgeries on three-tangle pretzel knots. https://doi.org/10.2140/agt.2009.9.743

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