Khovanov Homology and Conway Mutation

TL;DR

This paper provides an example of mutant links with differing Khovanov homology, highlighting limitations in defining Khovanov homology via skein relations similar to the Jones polynomial.

Contribution

It presents the first explicit example of mutant links with different Khovanov homology, demonstrating a fundamental difference from skein-based invariants.

Findings

Mutant links can have different Khovanov homology.

Khovanov homology cannot be defined by a skein rule like the Jones polynomial.

The example clarifies limitations of skein-based definitions.

Abstract

We present an easy example of mutant links with different Khovanov homology. The existence of such an example is important because it shows that Khovanov homology cannot be defined with a skein rule similar to the skein relation for the Jones polynomial.