Calculating Bar-Natan's characteristic two Khovanov homology

TL;DR

This paper explores Bar-Natan's characteristic two Khovanov homology, explicitly computing the filtered version and analyzing the bi-graded version using spectral sequences, revealing new structural insights.

Contribution

It provides explicit computations of the filtered theory and introduces a spectral sequence framework for analyzing the bi-graded theory in characteristic two.

Findings

Explicit computation of the filtered Khovanov homology

Description of E_2-pages via endomorphism actions

Discussion of simple consequences of the theory

Abstract

We investigate Bar-Natan's characteristic two Khovanov link homology theory studying both the filtered and bi-graded theories. The filtered theory is computed explicitly and the bi-graded theory analysed by setting up a family of spectral sequences. The E_2-pages can be described in terms of groups arising from the action of a certain endomorphism on mod 2 Khovanov homology. Some simple consequences are discussed.