We show that two-bridge knots and alternating fibered knots admit no purely cosmetic surgeries, ie no pair of distinct Dehn surgeries on such a knot produce –manifolds that are homeomorphic as oriented manifolds. Our argument, based on a recent result by Hanselman, uses several invariants of knots or –manifolds; for knots, we study the signature and some finite type invariants, and for –manifolds, we deploy the Casson invariant.
Kazuhiro Ichihara. In Dae Jong. Thomas W Mattman. Toshio Saito. "Two-bridge knots admit no purely cosmetic surgeries." Algebr. Geom. Topol. 21 (5) 2411 - 2424, 2021. https://doi.org/10.2140/agt.2021.21.2411