{
  "abstract": "We present a method to build free immersions in critical dimension on $m$-tori for $m = 2, 3, 4, 5$ by using a factorization trick inspired by tori immersions in critical dimension. As an application, we show that the set of smooth free maps from a closed surface $M$ to $\\mathbb R^5$ is nonempty. In particular, every closed surface embeds freely in $\\mathbb R^5$. Finally, we find the homotopy invariants of free maps in our environment and study which invariants are achieved by our maps.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.24610",
  "author_total": 1,
  "authors": [
    {
      "name": "Roberto De Leo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cv5wm0d0jcezd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.24610",
  "fulltext_url": null,
  "id": "cv5wm0d0jcezd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.24610",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
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  "openalex": "W7162452731",
  "pdf_url": "https://arxiv.org/pdf/2605.24610",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cv5wm0d0jcezd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2605.24610",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.24610"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Free maps in critical dimension on low-dimensional tori and closed surfaces",
  "title_text": "Free maps in critical dimension on low-dimensional tori and closed surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/cv5wm0d0jcezd",
  "venue": "arXiv",
  "versions": []
}