Pretzel links, mutation, and the slice-ribbon conjecture

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

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arXiv · 1805.02885

Pretzel links, mutation, and the slice-ribbon conjecture

Paolo Aceto·Min Hoon Kim·JungHwan Park·Arunima Ray

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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.

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Paolo Aceto, Min Hoon Kim, JungHwan Park, Arunima Ray. 2018-05-08. Pretzel links, mutation, and the slice-ribbon conjecture. https://arxiv.org/abs/1805.02885

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