{
  "id": "0707.4118",
  "version": "v1",
  "published": "2007-07-27T13:59:38.000Z",
  "updated": "2007-07-27T13:59:38.000Z",
  "title": "The Hochschild cohomology of a Poincaré algebra",
  "authors": [
    "Po Hu"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "In this note, we define the notion of a cactus set, and show that its geometric realization is naturally an algebra over Voronov's cactus operad, which is equivalent to the framed 2-dimensional little disks operad $\\mathcal{D}_2$. Using this, we show that the Hochschild cohomology of a Poincar\\'e algebra A is an algebra over (the chain complexes of) $\\mathcal{D}_2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-27T13:59:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P48",
      "16E40"
    ],
    "keywords": [
      "hochschild cohomology",
      "little disks operad",
      "voronovs cactus operad",
      "cactus set",
      "geometric realization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.4118H"
    }
  }
}