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2009 Finite surgeries on three-tangle pretzel knots
David Futer, Masaharu Ishikawa, Yuichi Kabaya, Thomas W Mattman, Koya Shimokawa
Algebr. Geom. Topol. 9(2): 743-771 (2009). DOI: 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,)–character variety. In particular, we introduce new techniques for demonstrating that boundary slopes are detected by the character variety.

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David Futer. Masaharu Ishikawa. Yuichi Kabaya. Thomas W Mattman. Koya Shimokawa. "Finite surgeries on three-tangle pretzel knots." Algebr. Geom. Topol. 9 (2) 743 - 771, 2009. https://doi.org/10.2140/agt.2009.9.743

Information

Received: 29 September 2008; Accepted: 10 February 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1166.57003
MathSciNet: MR2496889
Digital Object Identifier: 10.2140/agt.2009.9.743

Subjects:
Primary: 57M05, 57M25, 57M50

Rights: Copyright © 2009 Mathematical Sciences Publishers

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Vol.9 • No. 2 • 2009
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