CALCULATING BAR-NATAN'S CHARACTERISTIC TWO KHOVANOV HOMOLOGY

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 E2-pages can be described in terms of groups arising from the action of a certain endomorphism on 𝔽2-Khovanov homology. Some simple consequences are discussed.