{
  "id": "1211.6833",
  "version": "v2",
  "published": "2012-11-29T07:50:08.000Z",
  "updated": "2013-04-25T04:26:51.000Z",
  "title": "Derived string topology and the Eilenberg-Moore spectral sequence",
  "authors": [
    "Katsuhiko Kuribayashi",
    "Luc Menichi",
    "Takahito Naito"
  ],
  "comment": "40 pages, this version is one of two preprints divided from the first version, an appendix on shriek maps is revised",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let $M$ be any simply-connected Gorenstein space over any field. F\\'elix and Thomas have extended to simply-connected Gorenstein spaces, the loop (co)products of Chas and Sullivan on the homology of the free loop space $H_*(LM)$. We describe these loop (co)products in terms of the torsion and extension functors by developing string topology in appropriate derived categories. As a consequence, we show that the Eilenberg-Moore spectral sequence converging to the loop homology of a Gorenstein space admits a multiplication and a comultiplication with shifted degree which are compatible with the loop product and the loop coproduct of its target, respectively. We also define a generalized cup product on the Hochschild cohomology $HH^*(A,A^\\vee)$ of a commutative Gorenstein algebra $A$ and show that over $\\mathbb{Q}$, $HH^*(A_{PL}(M),A_{PL}(M)^\\vee)$ is isomorphic as algebras to $H_*(LM)$. Thus, when $M$ is a Poincar\\'e duality space, we recover the isomorphism of algebras $\\mathbb{H}_*(LM;\\mathbb{Q})^\\cong HH^*(A_{PL}(M),A_{PL}(M))$ of F\\'elix and Thomas.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-25T04:26:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "eilenberg-moore spectral sequence",
      "derived string topology",
      "simply-connected gorenstein space",
      "free loop space",
      "gorenstein space admits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1204862,
      "adsabs": "2012arXiv1211.6833K"
    }
  }
}