The Bar-Natan Theory Splits

Abstract

We show that over the binary field ${\mathbb{F}}_2$, the Bar-Natan perturbation of Khovanov homology splits as the direct sum of its two reduced theories, which we also prove are isomorphic. This extends Shumakovitch's analogous result for ordinary Khovanov homology, without the perturbation.

References in corpus (1)

• A geometric spectral sequence in Khovanov homology