{
  "id": "1510.00822",
  "version": "v1",
  "published": "2015-10-03T13:47:44.000Z",
  "updated": "2015-10-03T13:47:44.000Z",
  "title": "Graphs in the 3--sphere with maximum symmetry",
  "authors": [
    "Chao Wang",
    "Shicheng Wang",
    "Yimu Zhang",
    "Bruno Zimmermann"
  ],
  "comment": "33 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We consider the orientation preserving actions of finite groups $G$ on pairs $(S^3, \\Gamma)$, where $\\Gamma$ is a connected graph of genus $g>1$, embedded in $S^3$. For each $g$ we give the maximum order $m_g$ of such $G$ acting on $(S^3, \\Gamma)$ for all such $\\Gamma\\subset S^3$. Indeed we will classify all graphs $\\Gamma\\subset S^3$ which realize these $m_g$ in different levels: as abstract graphs and as spatial graphs, as well as their group actions. Such maximum orders without the condition \"orientation preserving\" are also addressed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-03T13:47:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M60",
      "57S17",
      "57S25"
    ],
    "keywords": [
      "maximum symmetry",
      "maximum order",
      "group actions",
      "finite groups",
      "spatial graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}