Pretzel links, mutation, and the slice-ribbon conjecture

Aceto, Paolo; Kim, Min Hoon; Park, JungHwan; Ray, Arunima

doi:10.4310/MRL.2021.v28.n4.a1

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Pretzel links, mutation, and the slice-ribbon conjecture

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Kim, Min Hoon
Max Planck Institute for Mathematics, Max Planck Society;

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Ray, Arunima
Max Planck Institute for Mathematics, Max Planck Society;

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https://dx.doi.org/10.4310/MRL.2021.v28.n4.a1
(Publisher version)

https://doi.org/10.48550/arXiv.1805.02885
(Preprint)

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Citation

Aceto, P., Kim, M. H., Park, J., & Ray, A. (2021). Pretzel links, mutation, and the slice-ribbon conjecture. Mathematical Research Letters, 28(4), 945-966. doi:10.4310/MRL.2021.v28.n4.a1.

Cite as: https://hdl.handle.net/21.11116/0000-0009-B8AA-8

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.