{
  "id": "0906.4245",
  "version": "v1",
  "published": "2009-06-23T12:53:57.000Z",
  "updated": "2009-06-23T12:53:57.000Z",
  "title": "On a Generalization of Alexander Polynomial for Long Virtual Knots",
  "authors": [
    "Afanasiev Denis"
  ],
  "comment": "5 pages, 1 figure",
  "categories": [
    "math.GT"
  ],
  "abstract": "We construct new invariant polynomial for long virtual knots. It is a generalization of Alexander polynomial. We designate it by $\\zeta$ meaning an analogy with $\\zeta$-polynomial for virtual links. A degree of $\\zeta$-polynomial estimates a virtual crossing number. We describe some application of $\\zeta$-polynomial for the study of minimal long virtual diagrams with respect number of virtual crossings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-23T12:53:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "long virtual knots",
      "alexander polynomial",
      "generalization",
      "minimal long virtual diagrams",
      "respect number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.4245D"
    }
  }
}