{
  "id": "math/0606231",
  "version": "v1",
  "published": "2006-06-09T21:28:00.000Z",
  "updated": "2006-06-09T21:28:00.000Z",
  "title": "Intrinsic Linking and Knotting in Virtual Spatial Graphs",
  "authors": [
    "Thomas Fleming",
    "Blake Mellor"
  ],
  "comment": "13 pages, 13 figures",
  "journal": "Alg. Geom. Top., Vol. 7, 2007, pp. 583-601",
  "categories": [
    "math.GT",
    "math.CO"
  ],
  "abstract": "We introduce a notion of intrinsic linking and knotting for virtual spatial graphs. Our theory gives two filtrations of the set of all graphs, allowing us to measure, in a sense, how intrinsically linked or knotted a graph is; we show that these filtrations are descending and non-terminating. We also provide several examples of intrinsically virtually linked and knotted graphs. As a byproduct, we introduce the {\\it virtual unknotting number} of a knot, and show that any knot with non-trivial Jones polynomial has virtual unknotting number at least 2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-09T21:28:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M15",
      "05C10"
    ],
    "keywords": [
      "virtual spatial graphs",
      "intrinsic linking",
      "virtual unknotting number",
      "non-trivial jones polynomial",
      "filtrations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6231F"
    }
  }
}