Two-Bridge Knots Admit no Purely Cosmetic Surgeries (Thomas Mattman, California State University, Chico)

(Joint with Ichihara, Jong, and Saito). We show that two-bridge knots admit no purely cosmetic surgeries, ie no pair of distinct Dehn surgeries on such a knot produce 3-manifolds that are homeomorphic as oriented manifolds. Our argument is based on a recent result by Hanselman and a study of signature and finite type invariants of knots as well as the SL(2,\C) Casson invariant.