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 $K'$, for some $n>1$, then either the genus of $K$ is larger than that of $K'$ or $K$ is isotopic to $K'$.

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