{
  "id": "0908.1538",
  "version": "v1",
  "published": "2009-08-11T17:52:24.000Z",
  "updated": "2009-08-11T17:52:24.000Z",
  "title": "Twist Lattices and the Jones-Kauffman Polynomial for Long Virtual Knots",
  "authors": [
    "Micah W. Chrisman"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, we investigate twist sequences for Kauffman finite-type invariants and Goussarov-Polyak-Viro finite-type invariants. It is shown that one obtains a Kauffman or GPV type of degree $\\le n$ if and only if an invariant is a polynomial of degree $\\le n$ on every twist lattice of the right form. The main result of this paper is an application of this technique to the coefficients of the Jones-Kauffman polynomial. It is shown that the Kauffman finite-type invariants obtained from these coefficients are not GPV finite-type invariants of any degree by explicitly showing they can never be polynomials. This generalizes a result of Kauffman, where it is known for degree $k=2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-11T17:52:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "long virtual knots",
      "jones-kauffman polynomial",
      "twist lattice",
      "kauffman finite-type invariants",
      "goussarov-polyak-viro finite-type invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.1538C"
    }
  }
}