Knot Floer homology obstructs ribbon concordance

• 成果类型: Article
• 署名作者: Zemke, Ian
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2019.190.3.5
• 发表日期: 2019
• 页码: 931-947
• 关键词: HOLOMORPHIC DISKS; LINK COBORDISMS; genus; functoriality; INVARIANTS; MAPS

摘要

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.