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

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

Cite this