Cosmetic crossing conjecture for genus one knots with non-trivial Alexander polynomial

Abstract

We prove the cosmetic crossing conjecture for genus one knots with non-trivial Alexander polynomial. We also prove the conjecture for genus one knots with trivial Alexander polynomial, under some additional assumptions.

arXiv comment6 pages, 1 figure

References in corpus (2)

• The lines of the Kontsevich integral and Rozansky's rationality conjecture
• Cosmetic crossings and Seifert matrices

Cited by in corpus (3)

• Applications of the Casson-Walker invariant to the knot complement and the cosmetic crossing conjectures
• Cosmetic operations and Khovanov multicurves
• On the Cosmetic Crossing Conjecture for Special Alternating Links