# A refinement of Khovanov homology

## TL;DR

This paper introduces a triply-graded refinement of Khovanov homology for links with involutions, enabling detection of mutation, especially in strongly invertible knots, thus enhancing the invariants' sensitivity.

## Contribution

It develops a new triply-graded Khovanov homology refinement that detects mutation in strongly invertible knots, advancing link invariants.

## Key findings

- Refinement detects mutation in strongly invertible knots.
- Triply-graded theory arises from a pair of filtrations.
- Enhances the sensitivity of Khovanov homology.

## Abstract

We refine Khovanov homology in the presence of an involution on the link. This refinement takes the form of a triply-graded theory, arising from a pair of filtrations. We focus primarily on strongly invertible knots and show, for instance, that this refinement is able to detect mutation.