{
  "id": "0908.1013",
  "version": "v1",
  "published": "2009-08-07T10:13:23.000Z",
  "updated": "2009-08-07T10:13:23.000Z",
  "title": "String topology for complex projective spaces",
  "authors": [
    "Richard A. Hepworth"
  ],
  "comment": "41 pages",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "In 1999 Chas and Sullivan showed that the homology of the free loop space of an oriented manifold admits the structure of a Batalin-Vilkovisky algebra. In this paper we give a complete description of this Batalin-Vilkovisky algebra for complex projective spaces. This builds on a description of the ring structure that is due to Cohen, Jones and Yan. In the course of the proof we establish several new general results. These include a description of how symmetries of a manifold can be used to understand its string topology, and a relationship between characteristic classes and circle actions on sphere bundles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-07T10:13:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R19",
      "58D99"
    ],
    "keywords": [
      "complex projective spaces",
      "string topology",
      "batalin-vilkovisky algebra",
      "free loop space",
      "sphere bundles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 828216,
      "adsabs": "2009arXiv0908.1013H"
    }
  }
}