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’s diagonalization theorem. As a consequence, we prove the slice-ribbon conjecture for 4-stranded 2-component pretzel links. © 2021 International Press of Boston, Inc.. All rights reserved.