{
  "abstract": "We construct metrics of strictly positive sectional curvature on at least 508 pairwise nondiffeomorphic exotic fifteen-spheres, without prescribing orientations. The construction begins with quaternionic line bundles over $\\mathbb{H}P^2\\times S^4$. Surgery along a Hopf fiber gives homotopy spheres with specified equivariant two-disk presentations. A calculation on the surgery filling distinguishes 1015 nonstandard oriented smooth types. We construct positively curved quotient metrics on both disks, match their boundary data under the prescribed attaching map, and smooth the seam by averaging the inverse tangential metrics. The connection estimates and the smoothing argument are proved directly for every two-plane. Thus the curvature conclusion does not require a compatible-disk theorem from the eleven-dimensional construction or an external curvature-gluing theorem. We give quantitative parameter bounds and specify the auxiliary choices for the first nontrivial member after fixing its smooth gauge family.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03310",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhiqi Chen"
    },
    {
      "name": "Shaoqiang Deng"
    },
    {
      "name": "Hui Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2q0c4625hpghx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03310",
  "fulltext_url": null,
  "id": "2q0c4625hpghx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03310",
  "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.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7220362368",
  "pdf_url": "https://arxiv.org/pdf/2610.03310",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2q0c4625hpghx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.03310",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03310"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Positive sectional curvature on a family of exotic fifteen-sphere",
  "title_text": "Positive sectional curvature on a family of exotic fifteen-sphere",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/2q0c4625hpghx",
  "venue": "arXiv",
  "versions": []
}