{
  "id": "1507.03312",
  "version": "v1",
  "published": "2015-07-13T02:51:46.000Z",
  "updated": "2015-07-13T02:51:46.000Z",
  "title": "Automorphisms of braid groups on orientable surfaces",
  "authors": [
    "Byunghee An"
  ],
  "comment": "22 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper we compute the automorphism groups $\\operatorname{Aut}(\\mathbf{P}_n(\\Sigma))$ and $\\operatorname{Aut}(\\mathbf{B}_n(\\Sigma))$ of braid groups $\\mathbf{P}_n(\\Sigma)$ and $\\mathbf{B}_n(\\Sigma)$ on every orientable surface $\\Sigma$, which are isomorphic to group extensions of the extended mapping class group $\\mathcal{M}^*_n(\\Sigma)$ by the transvection subgroup except for a few cases. We also prove that $\\mathbf{P}_n(\\Sigma)$ is always a characteristic subgroup of $\\mathbf{B}_n(\\Sigma)$ unless $\\Sigma$ is a twice-punctured sphere and $n=2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-13T02:51:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20F28",
      "32G15"
    ],
    "keywords": [
      "braid groups",
      "orientable surface",
      "extended mapping class group",
      "automorphism groups",
      "group extensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150703312A"
    }
  }
}