Abstract
We generalize Khovanov's homology to unoriented links and with coefficients in the 2-dimensional universal Frobenius algebra. Then, we construct, for each Reidemeister move, a graduated homotopy equivalence and give the explicit formulae of these equivalences and their homotopy inverses. Further, we prove that the generalized Khovanov complex of a link diagram D mirror image is isomorphic to the dual of the Khovanov complex of D. Finally, we generalize the Rasmussen theorem on the Lee–Khovanov homology.
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