{
  "id": "math/0107005",
  "version": "v1",
  "published": "2001-07-01T23:37:19.000Z",
  "updated": "2001-07-01T23:37:19.000Z",
  "title": "On the Jacobi Group and the Mapping Class Group of $S^3\\times S^3$",
  "authors": [
    "Nikolai A. Krylov"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "The paper containes a proof that the mapping class group of the manifold $S^3\\times S^3$ is isomorphic to a central extension of the (full) Jacobi group $\\Gamma^J$ by the group of 7-dimensional homotopy spheres. Using a presentation of the group $\\Gamma^J$ and the $\\mu$-invariant of the homotopy spheres, we give a presentation of the mapping class group of $S^3\\times S^3$ with generators and defining relations. We also compute cohomology of the group $\\Gamma^J$ and determine a 2-cocycle that corresponds to the mapping class group of $S^3\\times S^3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-07-01T23:37:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R50",
      "57R52",
      "20J06"
    ],
    "keywords": [
      "mapping class group",
      "jacobi group",
      "homotopy spheres",
      "central extension",
      "presentation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......7005K"
    }
  }
}