English

Pretzel links, mutation, and the slice-ribbon conjecture

Geometric Topology 2023-04-12 v2

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.

Cite

@article{arxiv.1805.02885,
  title  = {Pretzel links, mutation, and the slice-ribbon conjecture},
  author = {Paolo Aceto and Min Hoon Kim and JungHwan Park and Arunima Ray},
  journal= {arXiv preprint arXiv:1805.02885},
  year   = {2023}
}

Comments

14 pages, 7 figures, V2: Implements suggestions from a referee report. This version has been accepted for publication by MRL

R2 v1 2026-06-23T01:48:05.261Z