{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09937",
  "author_total": 1,
  "authors": [
    {
      "name": "Gakuto Kato"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9pctn3ta1gt0y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09937",
  "fulltext_url": null,
  "id": "9pctn3ta1gt0y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09937",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7212191243",
  "pdf_url": "https://arxiv.org/pdf/2609.09937",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9pctn3ta1gt0y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2609.09937",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09937"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Links and singularities of stable maps from $3$-manifolds to surfaces",
  "title_text": "Links and singularities of stable maps from $3$-manifolds to surfaces",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/9pctn3ta1gt0y",
  "venue": "arXiv",
  "versions": []
}