{
  "id": "math/0403145",
  "version": "v2",
  "published": "2004-03-08T23:59:37.000Z",
  "updated": "2005-06-18T22:02:59.000Z",
  "title": "Braid groups are almost co-Hopfian",
  "authors": [
    "Robert W. Bell",
    "Dan Margalit"
  ],
  "comment": "27 pages, 7 figures, improved exposition, minor corrections",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "Let B_n be the braid group on n > 3 strands. We prove that B_n modulo its center is co-Hopfian. We then show that any injective endomorphism of B_n is geometric in the sense that it is induced by a homeomorphism of a punctured disk. We further prove that any injection from B_n to B_n+1 is geometric. Additionally, we obtain analogous results for mapping class groups of punctured spheres. The methods use Thurston's theory of surface homeomorphisms and build upon work of Ivanov and McCarthy.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-06-18T22:02:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "57M07"
    ],
    "keywords": [
      "braid group",
      "co-hopfian",
      "mapping class groups",
      "thurstons theory",
      "surface homeomorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3145B"
    }
  }
}