{
  "id": "1011.4640",
  "version": "v4",
  "published": "2010-11-21T05:49:44.000Z",
  "updated": "2012-09-02T08:29:14.000Z",
  "title": "A Functorial Map from Virtual Knots to Classical Knots and Generalisations of Parity",
  "authors": [
    "Vassily Olegovich Manturov"
  ],
  "comment": "One key argument is corrected; new projections satisfying the same properties are constructed",
  "categories": [
    "math.GT"
  ],
  "abstract": "We construct various functorial maps (projections) from virtual knots to classical knots. These maps are defined on diagrams of virtual knots; in terms of Gauss diagram each of them can be represented as a deletion of some chords. The construction relies upon the notion of parity. As corollaries, we prove that the minimal classical crossing number for classical knots.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-09-02T08:29:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "virtual knots",
      "classical knots",
      "functorial map",
      "generalisations",
      "minimal classical crossing number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.4640O"
    }
  }
}