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 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. © 2009 Mathematical Sciences Publishers.