{
  "abstract": "We show that $S^2\\times S^4$ admits a complex structure. Starting from a modular family of complex two-tori associated with the $(3,4,\\infty)$ triangle group and the compactification constructed in [Alpöge 2026], we replace the period lattice by its unique monodromy-invariant index-two superlattice and compactify the resulting family. In the integral Mayer--Vietoris calculation, a primitive local class whose double is the class of a cusp component and the unique nonzero torsion class contributed by the multiplicity-four fibre restrict to the same class of order two on the common boundary. We then prove that the resulting compact complex threefold is diffeomorphic to $S^2\\times S^4$. The proof is discovered by the Odin Automatic AI Research Agent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05504",
  "author_total": 3,
  "authors": [
    {
      "name": "Shengtao Guo"
    },
    {
      "name": "Ethan X. Fang"
    },
    {
      "name": "Junwei Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e1hzd5yztf4np.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05504",
  "fulltext_url": null,
  "id": "e1hzd5yztf4np",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05504",
  "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.GM"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7212008999",
  "pdf_url": "https://arxiv.org/pdf/2609.05504",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e1hzd5yztf4np.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05504",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05504"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Geometry and complex manifolds",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Complex Structure on $S^2\\times S^4$",
  "title_text": "A Complex Structure on S^2× S^4",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/e1hzd5yztf4np",
  "venue": "arXiv",
  "versions": []
}