{
  "id": "0708.0066",
  "version": "v3",
  "published": "2007-08-01T04:44:09.000Z",
  "updated": "2009-10-14T14:16:42.000Z",
  "title": "Symmetries of spatial graphs and Simon invariants",
  "authors": [
    "Ryo Nikkuni",
    "Kouki Taniyama"
  ],
  "comment": "16 pages, 14 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "An ordered and oriented 2-component link L in the 3-sphere is said to be achiral if it is ambient isotopic to its mirror image ignoring the orientation and ordering of the components. Kirk-Livingston showed that if L is achiral then the linking number of L is not congruent to 2 modulo 4. In this paper we study orientation-preserving or reversing symmetries of 2-component links, spatial complete graphs on 5 vertices and spatial complete bipartite graphs on 3+3 vertices in detail, and determine the necessary conditions on linking numbers and Simon invariants for such links and spatial graphs to be symmetric.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-10-14T14:16:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M15",
      "57M25"
    ],
    "keywords": [
      "simon invariants",
      "spatial graphs",
      "symmetries",
      "spatial complete bipartite graphs",
      "linking number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.0066N"
    }
  }
}