{
  "abstract": "In this paper, we lift the instanton TQFT from ordinary categories to the $\\infty$-categorical setting by constructing a functor $CI:\\mathrm{BI}^{\\partial}\\longrightarrow\\mathsf{D}$ from an $\\infty$-cobordism category $\\mathrm{BI}^{\\partial}$ for instantons to an $\\infty$-derived category $\\mathsf{D}$ of $2$-periodic chain complexes. The construction of $\\mathrm{BI}^{\\partial}$ is a modification of the $\\infty$-cobordism category $\\mathrm{Bord}_4$ introduced by Lurie and by Calaque--Scheimbauer using complete Segal spaces. The target $\\infty$-category $\\mathsf{D}$ is obtained via the dg nerve of the dg category of $2$-periodic chain complexes of finitely presented projective $\\mathbb{Z}$-modules. The information encoded by the functor $CI$ was already developed by Kronheimer--Mrowka using families of metrics on cobordisms. Our reinterpretation in terms of $\\infty$-categories conceptually simplifies the construction of the hypercube complexes underlying the link spectral sequence. This viewpoint also clarifies hyperbox complexes and compression in Manolescu--Ozsváth's work, and possible $A_\\infty$-structures, especially their signs and higher coherence. In addition, we lift the generalized cap product $μ$-operators in instanton Floer homology to the chain level and construct explicit homotopies and higher homotopies establishing the commutativity of multiple $μ$-operators in even degrees.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.29902",
  "author_total": 1,
  "authors": [
    {
      "name": "Fan Ye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/53txd2sqmv64g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.29902",
  "fulltext_url": null,
  "id": "53txd2sqmv64g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.29902",
  "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.DG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
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      "openalex",
      "2608|Geometric and Algebraic Topology"
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  "openalex": "W7166650653",
  "pdf_url": "https://arxiv.org/pdf/2606.29902",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/53txd2sqmv64g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2606.29902",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.29902"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "An infinity-categorical TQFT from instantons",
  "title_text": "An infinity-categorical TQFT from instantons",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/53txd2sqmv64g",
  "venue": "arXiv",
  "versions": []
}