{
  "id": "1204.5390",
  "version": "v1",
  "published": "2012-04-24T14:37:16.000Z",
  "updated": "2012-04-24T14:37:16.000Z",
  "title": "The cohomology of the braid group B_3 and of SL_2(Z) with coefficients in a geometric representation",
  "authors": [
    "Filippo Callegaro",
    "Fred Cohen",
    "Mario Salvetti"
  ],
  "comment": "41 pages",
  "categories": [
    "math.AT",
    "math.GR"
  ],
  "abstract": "The purpose of this article is to describe the integral cohomology of the braid group B_3 and SL_2(Z) with local coefficients in a classical geometric representation given by symmetric powers of the natural symplectic representation. These groups have a description in terms of the so called \"divided polynomial algebra\". The results show a strong relation between torsion part of the computed cohomology and fibrations related to loop spaces of spheres.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-24T14:37:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N25",
      "20J06"
    ],
    "keywords": [
      "braid group",
      "natural symplectic representation",
      "loop spaces",
      "local coefficients",
      "classical geometric representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.5390C"
    }
  }
}