On the Cosmetic Crossing Conjecture for Special Alternating Links

Joe Boninger

doi:10.1090/bproc/184

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arXiv · 2302.12236

On the Cosmetic Crossing Conjecture for Special Alternating Links

Joe Boninger

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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 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.

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Joe Boninger. 2023-02-23. On the Cosmetic Crossing Conjecture for Special Alternating Links. https://doi.org/10.1090/bproc/184

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