{
  "abstract": "Let $M_{\\ell,m}=\\ell\\,\\mathbb{HP}^{2}\\# m\\,\\overline{\\mathbb{HP}^{2}}$ be the connected sum of $\\ell$ copies of $\\mathbb{HP}^{2}$ with $m$ copies of $\\mathbb{HP}^{2}$ endowed with the opposite orientation. We characterise, in terms of Pontryagin classes, the real vector bundles over $M_{\\ell,m}$ admitting a stable complex structure, and deduce that $M_{\\ell,m}$ is stably almost complex if and only if $\\ell-m$ is even. We then determine when an oriented real vector bundle of even rank over $M_{\\ell,m}$ admits a complex structure. Consequently, $M_{\\ell,m}$ admits an almost complex structure if and only if $\\ell=2m+1$ and $m$ is odd. This corrects an assertion made by Sato and Suzuki in 1974, according to which $M_{\\ell,m}$ is never almost complex. We also identify the unjustified step in their argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27929",
  "author_total": 1,
  "authors": [
    {
      "name": "Souvik Mandal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2brx5d3vz08qh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27929",
  "fulltext_url": null,
  "id": "2brx5d3vz08qh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27929",
  "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",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7214240562",
  "pdf_url": "https://arxiv.org/pdf/2609.27929",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2brx5d3vz08qh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27929",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27929"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Complex and Stable Complex Structures on Real Vector Bundles over Connected Sums of Quaternionic Projective Planes",
  "title_text": "Complex and Stable Complex Structures on Real Vector Bundles over Connected Sums of Quaternionic Projective Planes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/2brx5d3vz08qh",
  "venue": "arXiv",
  "versions": []
}