{
  "id": "math/0506375",
  "version": "v1",
  "published": "2005-06-19T14:28:15.000Z",
  "updated": "2005-06-19T14:28:15.000Z",
  "title": "Quasi-isometrically embedded subgroups of braid and diffeomorphism groups",
  "authors": [
    "John Crisp",
    "Bert Wiest"
  ],
  "comment": "23 pages, 6 figures",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We show that a large class of right-angled Artin groups (in particular, those with planar complementary defining graph) can be embedded quasi-isometrically in pure braid groups and in the group of area preserving diffeomorphisms of the disk fixing the boundary (with respect to the $L^2$-norm metric); this extends results of Benaim and Gambaudo who gave quasi-isometric embeddings of $F\\_n$ and $\\Z^n$ for all $n>0$. As a consequence we are also able to embed a variety of Gromov hyperbolic groups quasi-isometrically in pure braid groups and in the diffeomorphism group of the disk. Examples include hyperbolic surface groups, some HNN-extensions of these along cyclic subgroups and the fundamental group of a certain closed hyperbolic 3-manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-06-19T14:28:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "05C25"
    ],
    "keywords": [
      "diffeomorphism group",
      "quasi-isometrically embedded subgroups",
      "pure braid groups",
      "planar complementary defining graph",
      "hyperbolic surface groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......6375C"
    }
  }
}