Instantons and Bar-Natan homology

TL;DR

This paper introduces a spectral sequence connecting Bar-Natan's Khovanov homology to a deformation of instanton homology, revealing new relationships between knot invariants.

Contribution

It constructs a spectral sequence linking Bar-Natan's homology to instanton homology, expanding the understanding of their interplay in knot theory.

Findings

Spectral sequence from Bar-Natan's homology to instanton homology.

Specialization from characteristic-2 F5 homology.

New insights into knot invariants and their relationships.

Abstract

A spectral sequence is established, whose $E_{2}$ page is Bar-Natan's variant of Khovanov homology and which abuts to a deformation of instanton homology for knots and links. This spectral sequence arises as a specialization of a spectral sequence whose $E_{2}$ page is a characteristic-2 version of $F_{5}$ homology, in Khovanov's classification.