A mixed invariant of non-orientable surfaces in equivariant Khovanov homology

TL;DR

This paper introduces a new mixed invariant derived from deformations of Khovanov homology to distinguish non-orientable surfaces bounded by the same knot, including exotic cases.

Contribution

It constructs a novel invariant combining Lee and Bar-Natan deformations to differentiate non-orientable surfaces in knot theory.

Findings

Successfully distinguishes pairs of non-orientable surfaces with the same boundary knot

Identifies exotic non-orientable surfaces that previous invariants cannot distinguish

Provides new tools for studying surfaces in knot theory

Abstract

We construct a mixed invariant of non-orientable surfaces from the Lee and Bar-Natan deformations of Khovanov homology and use it to distinguish pairs of surfaces bounded by the same knot, including some exotic examples.