{
  "abstract": "We classify, up to almost diffeomorphism, the smooth closed oriented manifolds homotopy equivalent to each of the sphere products $S^{4k-1}\\times S^{4k}$, $S^{4k}\\times S^{4k}$, and $S^{4k}\\times S^{4k+1}$. In each case we realize the image of the normal-invariant map in the smooth surgery exact sequence by explicit families of manifolds: sphere bundles over $S^{4k}$; pinch maps and Milnor plumbings of disk bundles; and Novikov sphere bundles together with connected sums of homotopy spheres.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.10239",
  "author_total": 1,
  "authors": [
    {
      "name": "Sagnik Biswas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a8ggf2zce5stc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.10239",
  "fulltext_url": null,
  "id": "a8ggf2zce5stc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.10239",
  "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"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7164185956",
  "pdf_url": "https://arxiv.org/pdf/2606.10239",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a8ggf2zce5stc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2606.10239",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.10239"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Smooth manifolds homotopy equivalent to products of spheres",
  "title_text": "Smooth manifolds homotopy equivalent to products of spheres",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/a8ggf2zce5stc",
  "venue": "arXiv",
  "versions": []
}