The Knight Move Conjecture is false


الملخص بالإنكليزية

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).

تحميل البحث