{
  "id": "0801.0174",
  "version": "v3",
  "published": "2007-12-31T00:52:10.000Z",
  "updated": "2009-06-01T14:48:15.000Z",
  "title": "String topology of classifying spaces",
  "authors": [
    "David Chataur",
    "Luc Menichi"
  ],
  "comment": "53 pages. Section 3 on Props and fields theories rewritten. Section 4 expanded in new sections 4, 5, 6 and 7, to fix orientation problems, finite groups case detailed in section 7. Appendix on signs added. The rest of the sections almost unchanged. Some slight improvements on some results. For example, the BV-algebra is valid over any principal ideal domain",
  "categories": [
    "math.AT",
    "math.QA"
  ],
  "abstract": "Let $G$ be a finite group or a compact connected Lie group and let $BG$ be its classifying space. Let $\\mathcal{L}BG:=map(S^1,BG)$ be the free loop space of $BG$ i.e. the space of continuous maps from the circle $S^1$ to $BG$. The purpose of this paper is to study the singular homology $H_*(\\mathcal LBG)$ of this loop space. We prove that when taken with coefficients in a field the homology of $\\mathcal LBG$ is a homological conformal field theory. As a byproduct of our main theorem, we get a Batalin-Vilkovisky algebra structure on the cohomology $H^*(\\mathcal LBG)$. We also prove an algebraic version of this result by showing that the Hochschild cohomology $HH^*(S_* (G),S_*(G))$ of the singular chains of $G$ is a Batalin-Vilkovisky algebra.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-06-01T14:48:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18D50",
      "55N91",
      "55P35",
      "55P48",
      "55R12",
      "55R35",
      "55R40",
      "57R56",
      "58D29",
      "81T40",
      "81T45"
    ],
    "keywords": [
      "classifying space",
      "string topology",
      "batalin-vilkovisky algebra structure",
      "compact connected lie group",
      "homological conformal field theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 777074,
      "adsabs": "2008arXiv0801.0174C"
    }
  }
}