Finite surgeries on three-tangle pretzel knots

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

研究成果: Article査読

7 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)743-771
ページ数29
ジャーナルAlgebraic and Geometric Topology
9
2
DOI
出版ステータスPublished - 2009
外部発表はい

ASJC Scopus subject areas

  • 幾何学とトポロジー

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