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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Knot floer homology
- Ribbon concordance
- Seifert genus