Concordance homomorphisms from knot Floer homology

Peter S. Ozsváth; András I. Stipsicz; Zoltán Szabó

doi:10.1016/j.aim.2017.05.017

Concordance homomorphisms from knot Floer homology

Peter S. Ozsváth, András I. Stipsicz, Zoltán Szabó

Mathematics

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

87 Scopus citations

Abstract

We modify the construction of knot Floer homology to produce a one-parameter family of homologies tHFK for knots in S³. These invariants can be used to give homomorphisms from the smooth concordance group C to Z, giving bounds on the four-ball genus and the concordance genus of knots. We give some applications of these homomorphisms.

Original language	English (US)
Pages (from-to)	366-426
Number of pages	61
Journal	Advances in Mathematics
Volume	315
DOIs	https://doi.org/10.1016/j.aim.2017.05.017
State	Published - Jul 31 2017

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Concordance
Knot
Knot Floer homology
Knot homology

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10.1016/j.aim.2017.05.017

Cite this

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abstract = "We modify the construction of knot Floer homology to produce a one-parameter family of homologies tHFK for knots in S3. These invariants can be used to give homomorphisms from the smooth concordance group C to Z, giving bounds on the four-ball genus and the concordance genus of knots. We give some applications of these homomorphisms.",

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T1 - Concordance homomorphisms from knot Floer homology

AU - Ozsváth, Peter S.

AU - Stipsicz, András I.

AU - Szabó, Zoltán

PY - 2017/7/31

Y1 - 2017/7/31

N2 - We modify the construction of knot Floer homology to produce a one-parameter family of homologies tHFK for knots in S3. These invariants can be used to give homomorphisms from the smooth concordance group C to Z, giving bounds on the four-ball genus and the concordance genus of knots. We give some applications of these homomorphisms.

AB - We modify the construction of knot Floer homology to produce a one-parameter family of homologies tHFK for knots in S3. These invariants can be used to give homomorphisms from the smooth concordance group C to Z, giving bounds on the four-ball genus and the concordance genus of knots. We give some applications of these homomorphisms.

KW - Concordance

KW - Knot

KW - Knot Floer homology

KW - Knot homology

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M3 - Article

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SP - 366

EP - 426

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Concordance homomorphisms from knot Floer homology

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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