Joe Boninger
Published 2023-02-23Version 1
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 on crossing changes to knots with $L$-space branched double-covers, as well as tools from Scharlemann and Thompon's proof of the cosmetic crossing conjecture for the unknot.
Comments: 6 pages, 2 figures, comments welcome
Cosmetic crossing conjecture for genus one knots with non-trivial Alexander polynomial
Applications of the Casson-Walker invariant to the knot complement and the cosmetic crossing conjectures
An obstruction of Gordian distance one and cosmetic crossings for genus one knots
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