{
  "abstract": "We construct an explicit one-parameter family of smooth metrics on the Gromoll-Meyer exotic seven-sphere, converging in $C^\\infty$ to a fixed further Cheeger deformation of the Eschenburg-Kerin metric and having strictly positive sectional curvature for all sufficiently small positive parameter values. The first perturbation preserves the totally geodesic flats of one zero-plane family while making curvature positive near the other; the second removes the remaining zero curvature. The metric and the proof were discovered by the Odin Automatic AI Research Agent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12882",
  "author_total": 3,
  "authors": [
    {
      "name": "Shengtao Guo"
    },
    {
      "name": "Ethan X. Fang"
    },
    {
      "name": "Junwei Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4j02y6v5d4dwk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12882",
  "fulltext_url": null,
  "id": "4j02y6v5d4dwk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12882",
  "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.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7213169217",
  "pdf_url": "https://arxiv.org/pdf/2609.12882",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4j02y6v5d4dwk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12882",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12882"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Two-Stage Construction of Positive Curvature on the Gromoll-Meyer Sphere",
  "title_text": "A Two-Stage Construction of Positive Curvature on the Gromoll-Meyer Sphere",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/4j02y6v5d4dwk",
  "venue": "arXiv",
  "versions": []
}