{
  "id": "1608.03094",
  "version": "v1",
  "published": "2016-08-10T09:04:38.000Z",
  "updated": "2016-08-10T09:04:38.000Z",
  "title": "Rigidity and Flexibility for Handlebody Groups",
  "authors": [
    "Sebastian Hensel"
  ],
  "comment": "21 pages, 4 figures",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We show that finite index subgroups of the handlebody group are rigid in their ambient mapping class group: any injective map of a finite index subgroup of the genus $g$ handlebody group into the genus $g$ mapping class group is conjugation by a mapping class group element. On the other hand, we construct an injection of the genus $g$ handlebody group into a genus $h>g$ mapping class group which is not conjugate into a handlebody group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-10T09:04:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "handlebody group",
      "finite index subgroup",
      "flexibility",
      "ambient mapping class group",
      "mapping class group element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}