Cosmetic operations and Khovanov multicurves

Abstract

AbstractWe prove an equivariant version of the Cosmetic Surgery Conjecture for strongly invertible knots. Our proof combines a recent result of Hanselman with the Khovanov multicurve invariants $${\widetilde{{{\,\textrm{Kh}\,}}}}$$ Kh ~ and $${\widetilde{{{\,\textrm{BN}\,}}}}$$ BN ~ . We apply the same techniques to reprove a result of Wang about the Cosmetic Crossing Conjecture and split links. Along the way, we show that $${\widetilde{{{\,\textrm{Kh}\,}}}}$$ Kh ~ and $${\widetilde{{{\,\textrm{BN}\,}}}}$$ BN ~ detect if a Conway tangle is split.