{
  "abstract": "We show that two infinite families of homology $S^2\\times S^2$'s presented in \\cite{FPS, AP}, originally proposed as exotic candidates, are aspherical. In particular, none of these manifolds is an exotic $S^2\\times S^2$. We prove this by reconstructing them from aspherical building blocks, following Edmonds. The same arguments apply to and rule out further candidates for simply connected exotica. We also give counterexamples to the conjecture that Luttinger surgery preserves symplectic asphericity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04634",
  "author_total": 1,
  "authors": [
    {
      "name": "R. İnanç Baykur"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f0xm4xby2hnty.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04634",
  "fulltext_url": null,
  "id": "f0xm4xby2hnty",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04634",
  "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.GT"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7220711548",
  "pdf_url": "https://arxiv.org/pdf/2610.04634",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f0xm4xby2hnty.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.04634",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04634"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Exotic S^2 x S^2 candidates that are just fake",
  "title_text": "Exotic S^2 x S^2 candidates that are just fake",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/f0xm4xby2hnty",
  "venue": "arXiv",
  "versions": []
}