We give a geometric interpretation of the Khovanov complex for virtual links. Geometric interpretation means that we use a cobordism structure like D. Bar-Natan, but we allow non orientable cobordisms. Like D. Bar-Natans geometric complex our construction should work for virtual tangles too. This geometric complex allows, in contrast to the geometric version of V. Turaev and P. Turner, a direct extension of the classical Khovanov complex (h=t=0) and of the variant of Lee (h=0,t=1). Furthermore we give a classification of all unoriented TQFTs which can be used to define virtual link homologies with this geometric construction.
Journal of Knot Theory and Its Ramifications, 2014, Vol 23, Issue 9