On the cosmetic crossing conjecture for special alternating links

Abstract

We prove that a family of links, which includes all special alternating knots, does not admit non-nugatory crossing changes which preserve the isotopy type of the link. Our proof incorporates a result of Lidman and Moore [Trans. Amer. Math. Soc. 369 (2017), pp. 3639–3654] on crossing changes to knots with L L -space branched double-covers, as well as tools from Scharlemann and Thompson’s [Comment. Math. Helv. 64 (1989), pp. 527–535] proof of the cosmetic crossing conjecture for the unknot.