Cosmetic crossing changes of fibered knots

Abstract

We prove the nugatory crossing conjecture for fibered knots. We also show that if a knot $K$ is $n$-adjacent to a fibered knot $K^{\prime }$, for some $n>1$, then either the genus of $K$ is larger than that of $K^{\prime }$ or $K$ is isotopic to $K^{\prime }$.

Completely rewritten and shortened. To appear in J. Reine Angew. Math.(Crelle's Journal)

References in corpus (1)

• Bounded cohomology and non-uniform perfection of mapping class groups

Cited by in corpus (2)

• Cosmetic operations and Khovanov multicurves
• Crossing changes in closed 3-braid diagrams