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Mathematics > Geometric Topology

arXiv:2512.21825 (math)
[Submitted on 26 Dec 2025]

Title:Ribbon concordances and slice obstructions: experiments and examples

Authors:Nathan M. Dunfield, Sherry Gong
View a PDF of the paper titled Ribbon concordances and slice obstructions: experiments and examples, by Nathan M. Dunfield and Sherry Gong
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Abstract:There are 352.2 million prime knots in the 3-sphere with at most 19 crossings. We study which of these knots are slice, in both the smooth and topological categories. While no algorithm is known for deciding whether a given knot is slice in either setting, we are able to determine it smoothly for all but about 11,400 knots (0.003% or 1 in 30,000) and topologically for all but about 1,400 knots (0.0004% or about 1 in 250,000). In particular, we show that some 1.6 million of these knots (0.46%) are smoothly slice (in fact ribbon) and that 350.5 million are not even topologically slice (99.54%). We use a wide range of tools and techniques, and introduce several new or refined methods for probing these properties. Along the way, we produce 500,000 pairs of 0-friends, that is, pairs of distinct knots with the same 0-surgery. We discuss how our data is consistent with several important conjectures and suggests new ones, and highlight the simplest knots where sliceness remains unknown.
Comments: 62 pages, 24 figures, 12 tables
Subjects: Geometric Topology (math.GT)
MSC classes: 57K10 (Primary) 57K18, 57K32, 57K40, 57M99 (Secondary)
Cite as: arXiv:2512.21825 [math.GT]
  (or arXiv:2512.21825v1 [math.GT] for this version)
  https://doi.org/10.48550/arXiv.2512.21825
arXiv-issued DOI via DataCite

Submission history

From: Nathan M. Dunfield [view email]
[v1] Fri, 26 Dec 2025 01:47:29 UTC (1,655 KB)
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