Knot Floer homology obstructs ribbon concordance

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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.

Original languageEnglish (US)
Pages (from-to)931-947
Number of pages17
JournalAnnals of Mathematics
Issue number3
StatePublished - 2019

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Concordance
  • Knot floer homology
  • Ribbon concordance
  • Seifert genus


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