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As Oleg Viro describes in his paper, the most fundamental property of theKhovanov homology group is their invariance under Reidemeister moves. Viroconstructes Khovanov complex and homology consisting of Jordan curves with signand also gives a proof for the only case of first Reidemeister move by usinghis definition of Khovanov homology groups. In this paper, homotopy maps areobtained explicitly for the other Reidemeister moves, i.e. second and third.

On Reidemeister invariance of the Khovanov homology group of the Jones polynomial