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Mathematics > Geometric Topology

arXiv:1805.02885 (math)
[Submitted on 8 May 2018 (v1), last revised 11 Jul 2020 (this version, v2)]

Title:Pretzel links, mutation, and the slice-ribbon conjecture

Authors: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.
Comments: 14 pages, 7 figures, V2: Implements suggestions from a referee report. This version has been accepted for publication by MRL
Subjects: Geometric Topology (math.GT)
MSC classes: 57K40, 57K10
Report number: MPIM-Bonn-2018
Cite as: arXiv:1805.02885 [math.GT]
  (or arXiv:1805.02885v2 [math.GT] for this version)
  https://doi.org/10.48550/arXiv.1805.02885
Journal reference: Mathematical Research Letters 28 (2021), no. 4, 945-966

Submission history

From: JungHwan Park [view email]
[v1] Tue, 8 May 2018 08:15:02 UTC (236 KB)
[v2] Sat, 11 Jul 2020 15:37:12 UTC (437 KB)
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