{
  "id": "math/0502587",
  "version": "v1",
  "published": "2005-02-28T20:53:47.000Z",
  "updated": "2005-02-28T20:53:47.000Z",
  "title": "Bordism Invariants of the Mapping Class Group",
  "authors": [
    "Aaron Heap"
  ],
  "comment": "34 pages, 7 figures",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "We define new bordism and spin bordism invariants of certain subgroups of the mapping class group of a surface. In particular, they are invariants of the Johnson filtration of the mapping class group. The second and third terms of this filtration are the well-known Torelli group and Johnson subgroup, respectively. We introduce a new representation in terms of spin bordism, and we prove that this single representation contains all of the information given by the Johnson homomorphism, the Birman-Craggs homomorphism, and the Morita homomorphism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-02-28T20:53:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mapping class group",
      "spin bordism invariants",
      "single representation contains",
      "well-known torelli group",
      "johnson filtration"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2587H"
    }
  }
}