Pretzel links, mutation, and the slice-ribbon conjecture

Paolo Aceto; Min Hoon Kim; Jung Hwan Park; Arunima Ray

doi:10.4310/MRL.2021.V28.N4.A1

Pretzel links, mutation, and the slice-ribbon conjecture

Paolo Aceto, Min Hoon Kim, Jung Hwan Park, Arunima Ray

Department of Mathematics

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

2 Scopus citations

Abstract

Let p and q be distinct integers greater than one. We show that the 2-component pretzel link P (p, q, −p, −q) is not slice, even though it has a ribbon mutant, by using 3-fold branched covers and an obstruction based on Donaldson’s diagonalization theorem. As a consequence, we prove the slice-ribbon conjecture for 4-stranded 2-component pretzel links.

Original language	English
Pages (from-to)	945-966
Number of pages	22
Journal	Mathematical Research Letters
Volume	28
Issue number	4
DOIs	https://doi.org/10.4310/MRL.2021.V28.N4.A1
State	Published - 2021

Bibliographical note

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© 2021 International Press of Boston, Inc.. All rights reserved.

Access to Document

10.4310/MRL.2021.V28.N4.A1

Cite this

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title = "Pretzel links, mutation, and the slice-ribbon conjecture",

abstract = "Let p and q be distinct integers greater than one. We show that the 2-component pretzel link P (p, q, −p, −q) is not slice, even though it has a ribbon mutant, by using 3-fold branched covers and an obstruction based on Donaldson{\textquoteright}s diagonalization theorem. As a consequence, we prove the slice-ribbon conjecture for 4-stranded 2-component pretzel links.",

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AU - Aceto, Paolo

AU - Kim, Min Hoon

AU - Park, Jung Hwan

AU - Ray, Arunima

PY - 2021

Y1 - 2021

N2 - Let p and q be distinct integers greater than one. We show that the 2-component pretzel link P (p, q, −p, −q) is not slice, even though it has a ribbon mutant, by using 3-fold branched covers and an obstruction based on Donaldson’s diagonalization theorem. As a consequence, we prove the slice-ribbon conjecture for 4-stranded 2-component pretzel links.

AB - Let p and q be distinct integers greater than one. We show that the 2-component pretzel link P (p, q, −p, −q) is not slice, even though it has a ribbon mutant, by using 3-fold branched covers and an obstruction based on Donaldson’s diagonalization theorem. As a consequence, we prove the slice-ribbon conjecture for 4-stranded 2-component pretzel links.

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U2 - 10.4310/MRL.2021.V28.N4.A1

DO - 10.4310/MRL.2021.V28.N4.A1

M3 - Article

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SN - 1073-2780

VL - 28

SP - 945

EP - 966

JO - Mathematical Research Letters

JF - Mathematical Research Letters

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