{
  "id": "1205.1606",
  "version": "v1",
  "published": "2012-05-08T07:15:56.000Z",
  "updated": "2012-05-08T07:15:56.000Z",
  "title": "The braidings in the mapping class groups of surfaces",
  "authors": [
    "Yongjin Song"
  ],
  "comment": "11pages, 10 figures",
  "categories": [
    "math.AT"
  ],
  "abstract": "The disjoint union of mapping class groups of surfaces forms a braided monoidal category $\\mathcal M$, as the disjoint union of the braid groups $\\mathcal B$ does. We give a concrete, and geometric meaning of the braiding $\\beta_{r,s}$ in $\\M$. Moreover, we find a set of elements in the mapping class groups which correspond to the standard generators of the braid groups. Using this, we obtain an obvious map $\\phi:B_g\\ra\\Gamma_{g,1}$. We show that this map $\\phi$ is injective and nongeometric in the sense of Wajnryb. Since this map extends to a braided monoidal functor $\\Phi : \\mathcal B \\rightarrow \\mathcal M$, the integral homology homomorphism induced by $\\phi$ is trivial in the stable range.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-08T07:15:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R37",
      "18D10",
      "57M50"
    ],
    "keywords": [
      "mapping class groups",
      "braid groups",
      "disjoint union",
      "surfaces forms",
      "standard generators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.1606S"
    }
  }
}