{
  "id": "1704.05142",
  "version": "v1",
  "published": "2017-04-17T22:40:54.000Z",
  "updated": "2017-04-17T22:40:54.000Z",
  "title": "Surjective homomorphisms between surface braid groups",
  "authors": [
    "Lei Chen"
  ],
  "comment": "8 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $PB_n(S_{g,p})$ be the pure braid group of a genus $g>1$ surface with $p$ punctures. In this paper we prove that any surjective homomorphism $PB_n(S_{g,p})\\to PB_m(S_{g,p})$ factors through one of the forgetful homomorphisms. We then compute the automorphism group of $PB_n(S_{g,p})$, extending Irmak, Ivanov and McCarthy's result \\cite{ivanov} to the punctured case. Surprisingly, in contrast to the $n=1$ case, any automorphism of $PB_n(S_{g,p})$, $n>1$ is geometric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-17T22:40:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "surface braid groups",
      "surjective homomorphism",
      "pure braid group",
      "automorphism group",
      "mccarthys result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}