Abstract
We prove that the map on knot Floer homology induced by a ribbon concordance is injective. As a consequence, we prove that the Seifert genus is monotonic under ribbon concordance. Generalizing theorems of Gabai and Scharlemann, we also prove that the Seifert genus is super-additive under band connected sums of arbitrarily many knots. Our results give evidence for a conjecture of Gordon that ribbon concordance is a partial order on the set of knots.
Citation
Ian Zemke. "Knot Floer homology obstructs ribbon concordance." Ann. of Math. (2) 190 (3) 931 - 947, November 2019. https://doi.org/10.4007/annals.2019.190.3.5
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