{
  "abstract": "Work by David Reutter and Christopher Schommer-Pries has shown that ordinary smooth TQFTs can distinguish (stable) diffeomorphism classes of closed, connected, even-dimensional manifolds subject to certain finiteness conditions. In particular, simply connected, closed, smooth 6-manifolds with finite $π_2$ are diffeomorphic if and only if they cannot be distinguished by ordinary TQFTs. The question of whether or not this result holds for all simply connected closed 6-manifolds was open. We consider TQFTs out of the topological and smooth bordism categories, as well as out of a new bordism category constructed in this paper called the formally smooth (FS) bordism category. We present a pair of simply connected closed 6-manifolds with infinite $π_2$ that are not homotopy equivalent, yet are indistinguishable by ordinary TQFTs in all three categories. We extend this counter-example to show that ordinary TQFTs cannot distinguish the homotopy type of simply connected closed manifolds in all dimensions greater than or equal to 6 and non-simply connected closed 5-manifolds. We show that our class of counter-example pairs is spinnable and present a non-spinnable class of counter-examples by introducing a $\\mathbb{C}P^2$ connected summand. Lastly, we use more highly connected analogues of our counter-examples to show that, for all $n\\geq2$ and $m\\geq 2n$, there is a pair of $(2n-1)$-connected closed $(4n+m)$-manifolds that are not homotopy equivalent, yet cannot be distinguished by ordinary TQFTs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05480",
  "author_total": 1,
  "authors": [
    {
      "name": "Katherine Novey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7nz94z6g7tgpc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05480",
  "fulltext_url": null,
  "id": "7nz94z6g7tgpc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05480",
  "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"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7220675972",
  "pdf_url": "https://arxiv.org/pdf/2610.05480",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7nz94z6g7tgpc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05480",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05480"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Failure of Ordinary TQFTs to Distinguish Homotopy Type",
  "title_text": "Failure of Ordinary TQFTs to Distinguish Homotopy Type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/7nz94z6g7tgpc",
  "venue": "arXiv",
  "versions": []
}