Zredukowane homologie Khovanova

TL;DR

This paper introduces a natural, simplified reduction of Khovanov homology that generalizes previous reduced versions and applies to virtual knots, enhancing computational and theoretical utility.

Contribution

It proposes a new, natural reduction method for Khovanov homology that extends to virtual knots and links, unifying and simplifying existing approaches.

Findings

The reduction works for virtual knots and links.

It generalizes the reduced odd Khovanov homology.

Provides a more natural and straightforward reduction process.

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.