# Knot Floer homology obstructs ribbon concordance

## TL;DR

This paper demonstrates that knot Floer homology can be used to obstruct ribbon concordance, showing injectivity of the induced map and implications for Seifert genus monotonicity, supporting Gordon's conjecture.

## Contribution

It establishes the injectivity of the knot Floer homology map under ribbon concordance and proves the monotonicity of Seifert genus, advancing understanding of knot concordance relations.

## Key findings

- Knot Floer homology map is injective under ribbon concordance
- Seifert genus is monotonic under ribbon concordance
- Supports Gordon's conjecture on ribbon concordance as a partial order

## 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. We also generalize a theorem of Gabai about the super-additivity of the Seifert genus under band connected sum. Our result gives evidence for a conjecture of Gordon that ribbon concordance is a partial order on the set of knots.