On a construction of stable maps from 3-manifolds into surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918517083734016 |
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| author | Kato, Gakuto |
| author_facet | Kato, Gakuto |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21337 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a construction of stable maps from 3-manifolds into surfaces Kato, Gakuto Geometric Topology 57R45, 57M99, 57K10 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. |
| title | On a construction of stable maps from 3-manifolds into surfaces |
| topic | Geometric Topology 57R45, 57M99, 57K10 |
| url | https://arxiv.org/abs/2508.21337 |