{
  "abstract": "This paper presents a complete classification of the formality of configuration spaces of $\\mathbb{R}^{n'} \\times \\mathbb{C}^{n}$. We define a constructible de Rham-Dolbeault cohomology theory which provides a constructible CDGA (commutative differential graded algebra) model of $\\Conf_m(\\mathbb{R}^{n'} \\times \\mathbb{C}^{n})$. For $(n'=0,n\\ge2)$ or $(n'=1,n\\ge1)$, the CDGAs are non-formal. For $n'\\ge2,n\\ge1$, we establish an explicit quasi-isomorphism between the constructible CDGA and its cohomology by using a diagrammatic CDGA of admissible diagrams and a regularized configuration space integral, which leads to the formality. As an application, we show that the local operator algebra of a topological-holomorphic field theory on $\\mathbb{R}^{n'} \\times \\mathbb{C}^{n}$ ($n'\\ge2,n\\ge1$) is homotopically equivalent to a higher dimensional analog of vertex algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28200",
  "author_total": 3,
  "authors": [
    {
      "name": "Si Li"
    },
    {
      "name": "Peng Yang"
    },
    {
      "name": "Jiawei Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cp857jyvw3sbm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28200",
  "fulltext_url": null,
  "id": "cp857jyvw3sbm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28200",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
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  "openalex": "W7204835033",
  "pdf_url": "https://arxiv.org/pdf/2608.28200",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cp857jyvw3sbm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:22Z",
      "native_id": "2608.28200",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28200"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "On the Formality of Configuration Spaces of $\\mathbb{R}^{n'} \\times \\mathbb{C}^{n}$",
  "title_text": "On the Formality of Configuration Spaces of ℝ^n' × ℂ^n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/cp857jyvw3sbm",
  "venue": "arXiv",
  "versions": []
}