{
  "id": "math/0602108",
  "version": "v4",
  "published": "2006-02-06T21:26:15.000Z",
  "updated": "2007-03-14T12:55:21.000Z",
  "title": "String Bracket and Flat Connections",
  "authors": [
    "Hossein Abbaspour",
    "Mahmoud Zeinalian"
  ],
  "comment": "28 pages. This is the final version",
  "journal": "Algebraic & Geometric Topology Volume 7 (2007)",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "Let $G \\to P \\to M$ be a flat principal bundle over a closed and oriented manifold $M$ of dimension $m=2d$. We construct a map of Lie algebras $\\Psi: \\H_{2\\ast} (L M) \\to {\\o}(\\Mc)$, where $\\H_{2\\ast} (LM)$ is the even dimensional part of the equivariant homology of $LM$, the free loop space of $M$, and $\\Mc$ is the Maurer-Cartan moduli space of the graded differential Lie algebra $\\Omega^\\ast (M, \\adp)$, the differential forms with values in the associated adjoint bundle of $P$. For a 2-dimensional manifold $M$, our Lie algebra map reduces to that constructed by Goldman in \\cite{G2}. We treat different Lie algebra structures on $\\H_{2\\ast}(LM)$ depending on the choice of the linear reductive Lie group $G$ in our discussion.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2007-03-14T12:55:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P35",
      "57R19",
      "58A10",
      "57R22",
      "57N65",
      "55N33",
      "55N91"
    ],
    "keywords": [
      "flat connections",
      "string bracket",
      "lie algebra map reduces",
      "linear reductive lie group",
      "free loop space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2108A"
    }
  }
}