{
  "abstract": "Given a positive integer~$p$, we consider $W^{1,p}$-maps from a Euclidean domain of dimension $p+1$ into a closed Riemannian manifold $\\NN$. The target manifold is required to satisfy a suitable topological condition, that is, the action of the fundamental group over the~$p$-th homotopy group must be trivial; however, we do \\emph{not} assume that $\\NN$ is $(p-1)$-connected. Using tools from geometric measure theory --- namely, chains with coefficients in the $p$-th homotopy group of~$\\NN$--- we associate to each map a new object that captures its topological point singularities. We provide a characterisation of strong and weak sequential closures of smooth maps in~$W^{1,p}$ in terms of their topological singularities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.28622",
  "author_total": 2,
  "authors": [
    {
      "name": "Giacomo Canevari"
    },
    {
      "name": "Giandomenico Orlandi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1jr4dk2avb39g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.28622",
  "fulltext_url": null,
  "id": "1jr4dk2avb39g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.28622",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7162648389",
  "pdf_url": "https://arxiv.org/pdf/2605.28622",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1jr4dk2avb39g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:20Z",
      "native_id": "2605.28622",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.28622"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Topological point singularities of manifold-valued maps and approximability by smooth maps",
  "title_text": "Topological point singularities of manifold-valued maps and approximability by smooth maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:20Z",
  "url": "https://research.draconitic.com/paper/1jr4dk2avb39g",
  "venue": "arXiv",
  "versions": []
}