On Sutured Khovanov Homology and Axis-Preserving Mutations

TL;DR

This paper shows that sutured annular Khovanov homology changes under axis-preserving mutations of braid closures, revealing limitations of its invariance and connecting it to the Burau representation.

Contribution

It establishes the non-invariance of sutured annular Khovanov homology under axis-preserving mutations and links it explicitly to the Burau representation.

Findings

Sutured annular Khovanov homology is not invariant under axis-preserving mutations.

A direct relationship between sutured annular Khovanov homology and the Burau representation is demonstrated.

The result impacts the understanding of invariants in knot theory and their mutation sensitivity.

Abstract

This paper establishes that sutured annular Khovanov homology is not invariant for braid closures under axis-preserving mutations. This follows from an explicit relationship between sutured annular Khovanov homology and the classical Burau representation for braid closures.