{
  "id": "math/0309137",
  "version": "v4",
  "published": "2003-09-07T22:48:03.000Z",
  "updated": "2009-03-02T15:11:23.000Z",
  "title": "Rational maps and string topology",
  "authors": [
    "Sadok Kallel",
    "Paolo Salvatore"
  ],
  "comment": "This is the version published by Geometry & Topology on 28 October 2006",
  "journal": "Geom. Topol. 10 (2006) 1579-1606",
  "doi": "10.2140/gt.2006.10.1579",
  "categories": [
    "math.AT"
  ],
  "abstract": "We apply a version of the Chas-Sullivan-Cohen-Jones product on the higher loop homology of a manifold in order to compute the homology of the spaces of continuous and holomorphic maps of the Riemann sphere into a complex projective space. This product makes sense on the homology of maps from a co-H space to a manifold, and comes from a ring spectrum. We also build a holomorphic version of the product for maps of the Riemann sphere into homogeneous spaces. In the continuous case we define a related module structure on the homology of maps from a mapping cone into a manifold, and then describe a spectral sequence that can compute it. As a consequence we deduce a periodicity and dichotomy theorem when the source is a compact Riemann surface and the target is a complex projective space.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-03-02T15:11:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58D15",
      "26C15",
      "55R20"
    ],
    "keywords": [
      "rational maps",
      "string topology",
      "complex projective space",
      "riemann sphere",
      "higher loop homology"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......9137K"
    }
  }
}