Finite surgeries on three-tangle pretzel knots

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.