Concordance surgery and the Ozsváth–Szabó 4-manifold invariant

András Juhász; Ian Zemke

doi:10.4171/JEMS/1203

Concordance surgery and the Ozsváth–Szabó 4-manifold invariant

András Juhász
, Ian Zemke

Mathematics

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

2 Scopus citations

Abstract

We compute the effect of concordance surgery, a generalization of knot surgery defined using a self-concordance of a knot, on the Ozsváth–Szabó 4-manifold invariant. The formula involves the graded Lefschetz number of the concordance map on knot Floer homology. The proof uses the sutured Floer TQFT, and a version of sutured Floer homology perturbed by a 2-form.

Original language	English (US)
Pages (from-to)	995-1044
Number of pages	50
Journal	Journal of the European Mathematical Society
Volume	25
Issue number	3
DOIs	https://doi.org/10.4171/JEMS/1203
State	Published - 2023

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

4-manifolds
Heegaard Floer homology
concordance

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10.4171/JEMS/1203

Cite this

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title = "Concordance surgery and the Ozsv{\'a}th–Szab{\'o} 4-manifold invariant",

abstract = "We compute the effect of concordance surgery, a generalization of knot surgery defined using a self-concordance of a knot, on the Ozsv{\'a}th–Szab{\'o} 4-manifold invariant. The formula involves the graded Lefschetz number of the concordance map on knot Floer homology. The proof uses the sutured Floer TQFT, and a version of sutured Floer homology perturbed by a 2-form.",

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T1 - Concordance surgery and the Ozsváth–Szabó 4-manifold invariant

AU - Juhász, András

AU - Zemke, Ian

PY - 2023

Y1 - 2023

N2 - We compute the effect of concordance surgery, a generalization of knot surgery defined using a self-concordance of a knot, on the Ozsváth–Szabó 4-manifold invariant. The formula involves the graded Lefschetz number of the concordance map on knot Floer homology. The proof uses the sutured Floer TQFT, and a version of sutured Floer homology perturbed by a 2-form.

AB - We compute the effect of concordance surgery, a generalization of knot surgery defined using a self-concordance of a knot, on the Ozsváth–Szabó 4-manifold invariant. The formula involves the graded Lefschetz number of the concordance map on knot Floer homology. The proof uses the sutured Floer TQFT, and a version of sutured Floer homology perturbed by a 2-form.

KW - 4-manifolds

KW - Heegaard Floer homology

KW - concordance

UR - https://www.scopus.com/pages/publications/85153848531

UR - https://www.scopus.com/pages/publications/85153848531#tab=citedBy

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DO - 10.4171/JEMS/1203

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AN - SCOPUS:85153848531

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Concordance surgery and the Ozsváth–Szabó 4-manifold invariant

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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