{
  "id": "1009.0568",
  "version": "v4",
  "published": "2010-09-03T02:13:52.000Z",
  "updated": "2013-04-14T10:31:04.000Z",
  "title": "Automorphisms of the Torelli complex for the one-holed genus two surface",
  "authors": [
    "Yoshikata Kida",
    "Saeko Yamagata"
  ],
  "comment": "28 pages, 21 figures. Proof was largely modified because some hexagons had been overlooked (v3), Figures added and exposition improved (v4)",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Let S be a connected, compact and orientable surface of genus two having exactly one boundary component. We study automorphisms of the Torelli complex for S, and describe any isomorphism between finite index subgroups of the Torelli group for S. More generally, we study superinjective maps from the Torelli complex for S into itself, and show that any finite index subgroup of the Torelli group for S is co-Hopfian.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-04-14T10:31:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E36",
      "20F38"
    ],
    "keywords": [
      "torelli complex",
      "one-holed genus",
      "finite index subgroup",
      "torelli group",
      "boundary component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.0568K"
    }
  }
}