{
  "abstract": "We study spanning quadrangulations of even triangulations of real projective spaces, using the higher-dimensional notion of quadrangulation introduced by Kaiser and Stehl\\'ık. We prove that every even triangulation of $\\RP^d$, where $d\\ge 2$, admits a spanning bipartite quadrangulation. Moreover, such a triangulation admits a spanning non-bipartite quadrangulation if and only if it is not balanced; if it is balanced, every spanning quadrangulation is bipartite. Our proofs use coloring monodromy: its orbits yield bipartite quadrangulations, while a covering-space construction gives non-bipartite ones. %In dimension three, a bipartite quadrangulation can always be chosen to induce $K_{2,2}$ on each tetrahedron. More generally, we establish a sufficient condition for the existence of spanning bipartite quadrangulations on closed manifolds in terms of the monodromy action, and derive a consequence involving the fundamental group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29737",
  "author_total": 1,
  "authors": [
    {
      "name": "Kengo Enami"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0hqzr9xd5106s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29737",
  "fulltext_url": null,
  "id": "0hqzr9xd5106s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29737",
  "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.AT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7223238006",
  "pdf_url": "https://arxiv.org/pdf/2610.29737",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0hqzr9xd5106s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29737",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29737"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Spanning bipartite quadrangulations in even triangulations of real projective spaces",
  "title_text": "Spanning bipartite quadrangulations in even triangulations of real projective spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/0hqzr9xd5106s",
  "venue": "arXiv",
  "versions": []
}