{
  "abstract": "For integers $n\\ge 2$ and integers $\\ell,m\\ge 0$, not both zero, let $M^{4n}_{\\ell,m}=\\ell\\,\\mathbb{HP}^{n}\\,\\#\\,m\\,\\overline{\\mathbb{HP}^{n}}$ denote the connected sum of $\\ell$ copies of the quaternionic projective space $\\mathbb{HP}^{n}$ and $m$ copies of $\\mathbb{HP}^{n}$ endowed with the opposite orientation. By analysing the image of the complexification map $c\\,\\colon\\,\\widetilde{KO}(M^{4n}_{\\ell,m})\\to\\widetilde{K}(M^{4n}_{\\ell,m})$, we characterise, in terms of Pontryagin classes, the real vector bundles over $M^{4n}_{\\ell,m}$ admitting a stable complex structure, and deduce that $M^{4n}_{\\ell,m}$ is stably almost complex if and only if $n=2$ and $\\ell-m$ is even. Consequently no $M^{4n}_{\\ell,m}$ with $n\\ge 3$ admits an almost complex structure. Sato and Suzuki asserted the non-existence of almost complex structures on $M^{4n}_{\\ell,m}$ in 1974 for $3\\le n\\le 10$, except possibly when $n=3$ and $\\ell=3m+1$; we establish it for all $n\\ge 3$, and in the stronger form of stable almost complex structures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02147",
  "author_total": 1,
  "authors": [
    {
      "name": "Souvik Mandal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e8zagm7pnkffp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02147",
  "fulltext_url": null,
  "id": "e8zagm7pnkffp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02147",
  "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"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7215757793",
  "pdf_url": "https://arxiv.org/pdf/2610.02147",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e8zagm7pnkffp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.02147",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02147"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Stable Complex Structures On Real Vector Bundles Over Connected Sums Of Quaternionic Projective Spaces",
  "title_text": "Stable Complex Structures On Real Vector Bundles Over Connected Sums Of Quaternionic Projective Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/e8zagm7pnkffp",
  "venue": "arXiv",
  "versions": []
}