Finite surgeries on three-tangle pretzel knots

Details Finite surgeries on three-tangle pretzel knots Finite surgeries on three-tangle pretzel knots

2008-09-24

arxiv.org/abs/0809.4278v2

Algebraic & Geometric Topology 9 (2009), 743-771

Mathematics

Geometric Topology

18 pages, 15 figures v2 - minor revisions throughout

Scientific paper

10.2140/agt.2009.9.743

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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