{
  "id": "1512.00542",
  "version": "v1",
  "published": "2015-12-02T01:51:23.000Z",
  "updated": "2015-12-02T01:51:23.000Z",
  "title": "Quotient and blow-up of automorphisms of graphs of groups",
  "authors": [
    "Kaidi Ye"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "In this paper we study the quotient and \"blow-up\" of graph-of-groups $\\cal{G}$ and of their automorphisms $H: \\cal{G} \\rightarrow \\cal{G}$. We show that the existence of such a \"blow-up\" of $\\bar{H}: \\bar{\\cal{G}} \\rightarrow \\bar{\\cal{G}}$ relative to a given family of \"local\" graph-of-groups isomorphisms $H_{i}: \\cal{G}_{i} \\rightarrow \\cal{G}_{i}$ depends crucially on the $H_{i}$-conjugacy class of the correction term $\\delta(\\bar{E}_{i})$ for any edge $\\bar{E}_{i}$ of $\\bar{\\cal{G}}$, where $H$-congjugacy is a new but natural concept introduced here. As an application we obtain a criterion as to whether a partial Dehn twist can be blown up relative to local Dehn twists to give an actual Dehn twist.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-02T01:51:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "automorphisms",
      "actual dehn twist",
      "partial dehn twist",
      "local dehn twists",
      "conjugacy class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}