Finite surgeries on three-tangle pretzel knots

David Futer; Masaharu Ishikawa; Yuichi Kabaya; Thomas W. Mattman; Koya Shimokawa

doi:10.2140/agt.2009.9.743

Finite surgeries on three-tangle pretzel knots

David Futer, Masaharu Ishikawa, Yuichi Kabaya, Thomas W. Mattman, Koya Shimokawa

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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.

Original language	English
Pages (from-to)	743-771
Number of pages	29
Journal	Algebraic and Geometric Topology
Volume	9
Issue number	2
DOIs	https://doi.org/10.2140/agt.2009.9.743
Publication status	Published - 2009
Externally published	Yes

Keywords

Culler-shalen seminorm
Exceptional dehn surgery
Finite surgery
Pretzel knot

ASJC Scopus subject areas

Geometry and Topology

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10.2140/agt.2009.9.743

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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 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.",

keywords = "Culler-shalen seminorm, Exceptional dehn surgery, Finite surgery, Pretzel knot",

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T1 - Finite surgeries on three-tangle pretzel knots

AU - Futer, David

AU - Ishikawa, Masaharu

AU - Kabaya, Yuichi

AU - Mattman, Thomas W.

AU - Shimokawa, Koya

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Culler-shalen seminorm

KW - Exceptional dehn surgery

KW - Finite surgery

KW - Pretzel knot

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JO - Algebraic and Geometric Topology

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Finite surgeries on three-tangle pretzel knots

Abstract

Keywords

ASJC Scopus subject areas

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