Zredukowane homologie Khovanova

Abstract

From the very beginning the Khovanov homology appears to be one of the most important invariant of knots; for computational and theoretical reasons it would be useful to operate with reduced version of it - nevertheless the definition given by Khovanov appears to be not natural in a sense that it requires choices of circles in every resolution of knot diagram. We propose a definition that generalizes the reduced odd Khovanov homology defined by Rasmussen, Ozsvath and Szabo to the case of Putyra's chronological homology and therefore gives a simple and natural way to reduce the standard Khovanov homology. Surprisingly the construction works as well for virtual knots and links.