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Links and singularities of stable maps from $3$-manifolds to surfaces

  • Gakuto Kato
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Abstract

For any two links in the $3$-sphere, we provide a visual construction of a stable map f from the $3$-sphere to the Euclidean plane such that f has no cusp points, the set of definite (resp. indefinite) fold points of f is isotopic to the first (resp. second) given link, and f does not have a certain type of singular fibers. Moreover, we obtain a similar result for any $3$-manifold by setting the target space to the $2$-sphere.

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Cite

BibTeXRIS
BibTeX
@misc{kato2026links,
  title = {{Links and singularities of stable maps from $3$-manifolds to surfaces}},
  author = {Gakuto Kato},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.09937},
  eprint = {2609.09937},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09937},
}
RIS
TY  - UNPB
TI  - Links and singularities of stable maps from $3$-manifolds to surfaces
AU  - Gakuto Kato
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.09937
UR  - https://arxiv.org/abs/2609.09937
AB  - For any two links in the $3$-sphere, we provide a visual construction of a stable map f from the $3$-sphere to the Euclidean plane such that f has no cusp points, the set of definite (resp. indefinite) fold points of f is isotopic to the first (resp. second) given link, and f does not have a certain type of singular fibers. Moreover, we obtain a similar result for any $3$-manifold by setting the target space to the $2$-sphere.
ER  -