Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Knight Move Conjecture is false   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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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an