{
  "abstract": "We develop tools to compute moduli spaces of geometric functorial field theories as mapping spaces of equivariant simplicial presheaves. Given a d-dimensional geometric structure F, presented as a presheaf on the site of smooth families of d-manifolds, we define its Cartesian realization, which is an O(d)-equivariant simplicial presheaf on the site of Cartesian spaces. We use Cartesian realizations to present the moduli space of functorial field theories with geometric structure F as a mapping space between O(d)-equivariant simplicial presheaves. In a companion paper, we use this result to compute the moduli space of smooth one-dimensional oriented Riemannian functorial field theories valued in an arbitrary smooth symmetric monoidal infinity-category.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11812",
  "author_total": 2,
  "authors": [
    {
      "name": "Jacek Kenig"
    },
    {
      "name": "Dmitri Pavlov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5bcy6qgshmrzr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11812",
  "fulltext_url": null,
  "id": "5bcy6qgshmrzr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11812",
  "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-ph"
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      "arxiv",
      "math.AT"
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      "arxiv",
      "math.CT"
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      "arxiv",
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      "2610|Homotopy and Cohomology in Algebraic Topology"
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  "openalex": "W7212233919",
  "pdf_url": "https://arxiv.org/pdf/2609.11812",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5bcy6qgshmrzr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2609.11812",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11812"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Moduli spaces of geometric functorial field theories",
  "title_text": "Moduli spaces of geometric functorial field theories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/5bcy6qgshmrzr",
  "venue": "arXiv",
  "versions": []
}