We classify Dehn surgeries on pretzel knots that result in a manifold of finite fundamental group. The only hyperbolic pretzel knots that admit nontrivial finite surgeries are and . Agol and Lackenby’s –theorem reduces the argument to knots with small indices . We treat these using the Culler–Shalen norm of the –character variety. In particular, we introduce new techniques for demonstrating that boundary slopes are detected by the character variety.
"Finite surgeries on three-tangle pretzel knots." Algebr. Geom. Topol. 9 (2) 743 - 771, 2009. https://doi.org/10.2140/agt.2009.9.743