Finite surgeries on three-tangle pretzel knots

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 non-trivial 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.

18 pages, 15 figures v2 - minor revisions throughout

References in corpus (3)

• Angled decompositions of arborescent link complements
• Surgery obstructions from Khovanov homology
• Cyclic and finite surgeries on Montesinos knots

Cited by in corpus (7)

• Surgery obstructions from Khovanov homology
• Cyclic and finite surgeries on Montesinos knots
• Finite knot surgeries and Heegaard Floer homology
• Seifert fibered surgery on Montesinos knots
• Obstructing finite surgery
• Immersed surfaces and Seifert fibered surgery on Montesinos knots
• Exceptional surgeries on $(-2,p,p)$-pretzel knots