Abstract:For any link in the $3$-sphere, we give a visual construction of a stable map $f$ from the $3$-sphere into the real plane enjoying the following properties; $f$ has no cusp point, the set of definite fold points of $f$ is isotopic to the given link and $f$ only has certain type of fibers containing two indefinite fold points. As a corollary, we obtain a similar stable map from every closed orientable $3$-manifold into the $2$-sphere.
| Comments: | 14 pages, 16 figures |
| Subjects: | Geometric Topology (math.GT) |
| MSC classes: | 57R45, 57M99, 57K10 |
| Cite as: | arXiv:2508.21337 [math.GT] |
| (or arXiv:2508.21337v3 [math.GT] for this version) | |
| https://doi.org/10.48550/arXiv.2508.21337 arXiv-issued DOI via DataCite |
From: Gakuto Kato [view email]
[v1]
Fri, 29 Aug 2025 05:38:50 UTC (55 KB)
[v2]
Wed, 10 Dec 2025 11:08:04 UTC (54 KB)
[v3]
Fri, 22 May 2026 11:42:25 UTC (86 KB)
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