Some differentials on Khovanov–Rozansky homology

In [12; 13], Khovanov and Rozansky introduced a new class of homological knot invariants which generalize the original construction of the Khovanov homology [9]. In this paper, we investigate these KR–homologies and the relations between them. Our motivation was to give some substance to the conjectures made in Dunfield, Gukov and Rasmussen [3] about the behavior of these theories and their relation to the knot Floer homology. Although we are unable to say anything about the latter problem, we hope that we can at least shed some light on the structure of KR–homology.

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