2023/03/07 by Dunfield, Nathan M., Gong, Sherry, Hockenhull, Thomas +2
#57-11 (Primary) 57K14 (Secondary) #57K18 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2303.04233
For a ribbon knot, it is a folk conjecture that the rank of its knot Floer homology must be 1 modulo 8, and another folk conjecture says the same about reduced Khovanov homology. We give the first counter-examples to both of these folk conjectures, but at the same time present compelling evidence for new conjectures that either of these homologies must have rank congruent to 1 modulo 4 for any ribbon knot. We prove that each revised conjecture is equivalent to showing that taking the rank of the homology modulo 4 gives a homomorphism of the knot concordance group. We check the revised conjectures for 2.4 million ribbon knots, and also prove they hold for ribbon knots with fusion number 1.