{
  "abstract": "We prove that a polynomial mapping $\\mathbb{R}^2 \\to \\mathbb{R}^2$ with nowhere zero Jacobian determinant is a global diffeomorphism provided the preimage of large circles are connected. In higher dimensions this result fails and we present families of counterexamples. Yet, in dimension $3$ with codimension of Jelonek set greater than one, we prove that if the preimages of large spheres are connected, then the Jelonek set of the mapping is neither homeomorphic to a line nor can have a single end at infinity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33875",
  "author_total": 3,
  "authors": [
    {
      "name": "Francisco Braun"
    },
    {
      "name": "Zbigniew Jelonek"
    },
    {
      "name": "Maria Michalska"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3cps32wgdrmg5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33875",
  "fulltext_url": null,
  "id": "3cps32wgdrmg5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33875",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223780944",
  "pdf_url": "https://arxiv.org/pdf/2610.33875",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3cps32wgdrmg5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.33875",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33875"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Global invertibility of polynomial mappings and connectedness of preimages of large spheres",
  "title_text": "Global invertibility of polynomial mappings and connectedness of preimages of large spheres",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/3cps32wgdrmg5",
  "venue": "arXiv",
  "versions": []
}