{
  "id": "2404.01323",
  "version": "v1",
  "published": "2024-03-28T15:57:10.000Z",
  "updated": "2024-03-28T15:57:10.000Z",
  "title": "Batalin-Vilkovisky algebra structure on the Hochschild cohomology of $E_\\infty$-algebras",
  "authors": [
    "Ismaïl Razack"
  ],
  "comment": "38 pages, comments are welcome. arXiv admin note: substantial text overlap with arXiv:2305.19054",
  "categories": [
    "math.AT"
  ],
  "abstract": "When $\\mathcal{M}$ is a smooth, oriented, compact and simply connected manifold, Luc Menichi has shown that $HH^\\ast(C^\\ast(\\mathcal{M}; \\mathbb{F}))$, the Hochschild cohomology of the singular cochain complex of $\\mathcal{M}$ is a Batalin-Vilkovisky algebra. Using the properties of algebras over the Barratt-Eccles operad, we show that this results holds even when the manifold is not simply connected. Furthermore, we prove a similar result for pseudomanifolds. Namely, we explain why $HH^\\ast_\\bullet(\\widetilde N^\\ast_\\bullet(X;\\mathbb{F}))$, the Hochschild cohomology of the blown-up intersection cochain complex of a compact, oriented pseudomanifold $X$, is endowed with a Batalin-Vilkovisky algebra structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-28T15:57:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E40",
      "55N33"
    ],
    "keywords": [
      "batalin-vilkovisky algebra structure",
      "hochschild cohomology",
      "blown-up intersection cochain complex",
      "singular cochain complex",
      "pseudomanifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}