Cosmetic crossing changes of fibered knots

TL;DR

This paper proves the nugatory crossing conjecture for fibered knots and explores the relationship between knots that are n-adjacent to fibered knots, revealing genus constraints or isotopy.

Contribution

It establishes the nugatory crossing conjecture specifically for fibered knots and characterizes knots n-adjacent to fibered knots in terms of genus and isotopy.

Findings

Proves the nugatory crossing conjecture for fibered knots.

Shows that n-adjacency to a fibered knot implies genus inequality or isotopy.

Provides conditions under which knots are isotopic based on n-adjacency.

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 $K'$.