{
  "abstract": "For a given $n$-valued map, there exists a suitable minimal covering of the domain such that the composition of this covering with the map yields a split map, composed of $n$ single-valued maps, called the lift factors. Using the group action of the deck-transformation group we construct intermediate covering spaces as well as intermediate configuration spaces, allowing the original map to lift to these spaces, building a tower to illustrate at which level the lift factors split off. We then display two applications of these new tools. The first is to derive results concerning the Borsuk-Ulam property for certain coverings of the tower. The second is to obtain a sharp formula for the Nielsen number of an $n$-valued non-split map, using the coincidence number of specific single-valued maps that arise in the lifts of the tower.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34013",
  "author_total": 3,
  "authors": [
    {
      "name": "Daciberg Lima Gonçalves"
    },
    {
      "name": "Bartira Maués"
    },
    {
      "name": "Daniel Vendrúscolo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7zc153pe5xswe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34013",
  "fulltext_url": null,
  "id": "7zc153pe5xswe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34013",
  "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.AT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7214761076",
  "pdf_url": "https://arxiv.org/pdf/2609.34013",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7zc153pe5xswe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34013",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34013"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A study of $n$-valued non-split maps and applications",
  "title_text": "A study of n-valued non-split maps and applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/7zc153pe5xswe",
  "venue": "arXiv",
  "versions": []
}