Finite surgeries on three-tangle pretzel knots

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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)743-771
Number of pages29
JournalAlgebraic and Geometric Topology
Volume9
Issue number2
DOIs
Publication statusPublished - 2009 Dec 1
Externally publishedYes

Fingerprint

Pretzel Knot
Character Variety
Tangles
Surgery
Hyperbolic Knot
Dehn Surgery
Fundamental Group
Knot
Slope
Finite Group
Classify
Norm
Theorem

Keywords

  • Culler-shalen seminorm
  • Exceptional dehn surgery
  • Finite surgery
  • Pretzel knot

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Finite surgeries on three-tangle pretzel knots. / Futer, David; Ishikawa, Masaharu; Kabaya, Yuichi; Mattman, Thomas W.; Shimokawa, Koya.

In: Algebraic and Geometric Topology, Vol. 9, No. 2, 01.12.2009, p. 743-771.

Research output: Contribution to journalArticle

Futer, D, Ishikawa, M, Kabaya, Y, Mattman, TW & Shimokawa, K 2009, 'Finite surgeries on three-tangle pretzel knots', Algebraic and Geometric Topology, vol. 9, no. 2, pp. 743-771. https://doi.org/10.2140/agt.2009.9.743
Futer, David ; Ishikawa, Masaharu ; Kabaya, Yuichi ; Mattman, Thomas W. ; Shimokawa, Koya. / Finite surgeries on three-tangle pretzel knots. In: Algebraic and Geometric Topology. 2009 ; Vol. 9, No. 2. pp. 743-771.
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