{
  "abstract": "The cyclic homology of a $\\mathbb{Z}/2\\mathbb{Z}$-graded, smooth and proper $A_\\infty$ category satisfying the Hodge-to-de-Rham degeneration property carries the structure of a polarized semi-infinite Hodge structure or the so-called EP-structure. Given two $A_\\infty$ algebras $A$ and $B$ with the above conditions, we construct a Künneth map from the tensor product of their cyclic homologies to the cyclic homology of the $A_\\infty$ tensor product $A\\otimes_\\infty B$ and show that it respects the EP-structures. As an application, we show that if $A$ and $B$ are equipped with weak Calabi-Yau structures, then $A\\otimes_\\infty B$ also inherits a weak Calabi-Yau structure. Also, we show that the Künneth quasi-isomorphism respects good splittings of the Hodge filtration on $A$ and $B$ compatible with the weak Calabi-Yau structure. Our explicit calculations rely on the combinatorial (tree) description of the tensor product of $A_\\infty$ algebras developed in \\cite{amorim2016tensor}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30164",
  "author_total": 1,
  "authors": [
    {
      "name": "Henry Azubuike"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/atvpk54x2nngk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30164",
  "fulltext_url": null,
  "id": "atvpk54x2nngk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30164",
  "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.KT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7216643163",
  "pdf_url": "https://arxiv.org/pdf/2610.30164",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/atvpk54x2nngk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30164",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30164"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Künneth theorem for the cyclic homology of A-infinity algebras",
  "title_text": "A Künneth theorem for the cyclic homology of A-infinity algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/atvpk54x2nngk",
  "venue": "arXiv",
  "versions": []
}