{
  "id": "0707.4213",
  "version": "v5",
  "published": "2007-07-29T06:01:53.000Z",
  "updated": "2010-04-22T05:04:33.000Z",
  "title": "A Batalin-Vilkovisky Algebra structure on the Hochschild Cohomology of Truncated Polynomials",
  "authors": [
    "Tian Yang"
  ],
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "The main result of this paper is to calculate the Batalin-Vilkovisky structure of $HH^*(C^*(\\mathbf{K}P^n;R);C^*(\\mathbf{K}P^n;R))$ for $ \\mathbf{K}=\\mathbb{C}$ and $\\mathbb{H}$, and $R=\\mathbb{Z}$ and any field; and shows that in the special case when $M=\\mathbb{C}P^1=S^2$, and $R=\\mathbb{Z}$, this structure can not be identified with the BV-structure of $\\mathbb{H}_*(LS^2;\\mathbb{Z})$ computed by Luc Memichi in \\cite{menichi2}. However, the induced Gerstenhaber structures are still identified in this case. Moreover, according to a recent work of Y.Felix and J.Thomas \\cite{felix--thomas}, the main result of the present paper eventually calculates the BV-structure of the rational loop homology, $\\mathbb{H}_*(L\\mathbb{C}P^n;\\mathbb{Q})$ and $\\mathbb{H}_*(L\\mathbb{H}P^n;\\mathbb{Q})$, of projective spaces.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2010-04-22T05:04:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "batalin-vilkovisky algebra structure",
      "hochschild cohomology",
      "truncated polynomials",
      "main result",
      "rational loop homology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.4213Y"
    }
  }
}