Totally twisted Khovanov homology

Abstract

We define a variation of Khovanov homology formally similar to totally twisted Heegaard–Floer homology. Over a certain field, this version of Khovanov homology has a completely explicit description in terms of the spanning trees of a link projection. We prove that this new theory is a link invariant and describe some of its properties. Finally, we provide the results of some computer computations of the invariant.