The Knight Move Conjecture is false
Geometric Topology
2018-10-09 v2 Quantum Algebra
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).
Cite
@article{arxiv.1809.09769,
title = {The Knight Move Conjecture is false},
author = {Ciprian Manolescu and Marco Marengon},
journal= {arXiv preprint arXiv:1809.09769},
year = {2018}
}
Comments
4 pages; corrected a typo in Table 1