The Knight Move Conjecture is false
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- by Ciprian Manolescu and Marco Marengon PDF
- Proc. Amer. Math. Soc. 148 (2020), 435-439 Request permission
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 $\mathbb {Q}^2$ 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 non-trivial differential of bidegree $(1,8)$.References
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Additional Information
- Ciprian Manolescu
- Affiliation: Department of Mathematics, University of California Los Angeles, 520 Portola Plaza, Los Angeles, California 90095
- MR Author ID: 677111
- Email: cm@math.ucla.edu
- Marco Marengon
- Affiliation: Department of Mathematics, University of California Los Angeles, 520 Portola Plaza, Los Angeles, California 90095
- MR Author ID: 1171121
- Email: marengon@ucla.edu
- Received by editor(s): October 5, 2018
- Received by editor(s) in revised form: April 18, 2019
- Published electronically: July 10, 2019
- Additional Notes: The first author was partially supported by the NSF grant DMS-1708320.
- Communicated by: David Futer
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 435-439
- MSC (2010): Primary 57M27
- DOI: https://doi.org/10.1090/proc/14694
- MathSciNet review: 4042864