The Knight Move Conjecture is false


Abstract in English

The Knight Move Conjecture claims that the Khovanov homology of any knot decomposes as direct sums of some knight move pairs and a single pawn move pair. This is true for instance whenever the Lee spectral sequence from Khovanov homology to Q^2 converges on the second page, as it does for all alternating knots and knots with unknotting number at most 2. We present a counterexample to the Knight Move Conjecture. For this knot, the Lee spectral sequence admits a nontrivial differential of bidegree (1,8).

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