Ribbon concordances and slice obstructions: experiments and examples
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| author | Dunfield, Nathan M. Gong, Sherry |
| author_facet | Dunfield, Nathan M. Gong, Sherry |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21825 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ribbon concordances and slice obstructions: experiments and examples Dunfield, Nathan M. Gong, Sherry Geometric Topology 57K10 (Primary) 57K18, 57K32, 57K40, 57M99 (Secondary) 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. |
| title | Ribbon concordances and slice obstructions: experiments and examples |
| topic | Geometric Topology 57K10 (Primary) 57K18, 57K32, 57K40, 57M99 (Secondary) |
| url | https://arxiv.org/abs/2512.21825 |