Knot Floer homology obstructs ribbon concordance

Ian Zemke

doi:10.4007/annals.2019.190.3.5

Knot Floer homology obstructs ribbon concordance

Ian Zemke

Mathematics

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

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.

Original language	English (US)
Pages (from-to)	931-947
Number of pages	17
Journal	Annals of Mathematics
Volume	190
Issue number	3
DOIs	https://doi.org/10.4007/annals.2019.190.3.5
State	Published - 2019

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Concordance
Knot floer homology
Ribbon concordance
Seifert genus

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10.4007/annals.2019.190.3.5

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title = "Knot Floer homology obstructs ribbon concordance",

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.",

keywords = "Concordance, Knot floer homology, Ribbon concordance, Seifert genus",

author = "Ian Zemke",

note = "Publisher Copyright: {\textcopyright} 2019 Department of Mathematics, Princeton University.",

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language = "English (US)",

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T1 - Knot Floer homology obstructs ribbon concordance

AU - Zemke, Ian

PY - 2019

Y1 - 2019

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AB - 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.

KW - Concordance

KW - Knot floer homology

KW - Ribbon concordance

KW - Seifert genus

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JO - Annals of Mathematics

JF - Annals of Mathematics

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ER -

Knot Floer homology obstructs ribbon concordance

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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