The Knight Move Conjecture is false

Ciprian Manolescu; Marco Marengon

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arXiv · 1809.09769

The Knight Move Conjecture is false

Ciprian Manolescu·Marco Marengon

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Abstract

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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Ciprian Manolescu, Marco Marengon. 2018-09-26. The Knight Move Conjecture is false. https://arxiv.org/abs/1809.09769

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