Khovanov-Rozansky Homology and Conway Mutation

TL;DR

This paper proves that the reduced sl(n) homology, a knot invariant, remains unchanged under certain positive mutations when n is odd, enhancing understanding of knot invariants' behavior under mutation.

Contribution

It establishes the invariance of reduced sl(n) homology under component-preserving positive mutation for odd n, a new result in knot theory.

Findings

Reduced sl(n) homology is invariant under component-preserving positive mutation for odd n.

The invariance applies specifically to the case when n is odd.

This result advances the understanding of knot invariants under mutation.

Abstract

We show that the reduced sl(n) homology defined by Khovanov and Rozansky is invariant under component-preserving positive mutation when n is odd.