Contents Online
Mathematical Research Letters
Volume 28 (2021)
Number 4
Pretzel links, mutation, and the slice-ribbon conjecture
Pages: 945 – 966
DOI: https://dx.doi.org/10.4310/MRL.2021.v28.n4.a1
Authors
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.
Received 11 September 2019
Accepted 5 July 2020
Published 22 November 2021