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 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.

arXiv commentSome corrections and additions, now 7 pages and 3 figures

References in corpus (6)

• Alternating links and definite surfaces
• A characterisation of alternating knot exteriors
• Heegaard Floer homology and knots determined by their complements
• Applications of the Casson-Walker invariant to the knot complement and the cosmetic crossing conjectures
• Cosmetic crossing conjecture for genus one knots with non-trivial Alexander polynomial
• An obstruction of Gordian distance one and cosmetic crossings for genus one knots