{
  "id": "math/0402308",
  "version": "v1",
  "published": "2004-02-18T22:41:10.000Z",
  "updated": "2004-02-18T22:41:10.000Z",
  "title": "Virtual knots undetected by 1 and 2-strand bracket polynomials",
  "authors": [
    "H. A. Dye"
  ],
  "comment": "22 pages, 24 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Kishino's knot is not detected by the fundamental group or the bracket polynomial; these invariants cannot differentiate between Kishino's knot and the unknot. However, we can show that Kishino's knot is not equivalent to unknot by applying either the 3-strand bracket polynomial or the surface bracket polynomial. In this paper, we construct two non-trivial virtual knot diagrams, $ K_D $ and $ K_m $, that are not not detected by the bracket polynomial or the 2-strand bracket polynomial. From these diagrams, we construct two infinite families of non-classical virtual knot diagrams that are not detected by the bracket polynomial. Additionally, we note these virtual knot diagrams are trivial as flats.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-02-18T22:41:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "virtual knots",
      "kishinos knot",
      "non-trivial virtual knot diagrams",
      "surface bracket polynomial",
      "non-classical virtual knot diagrams"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2308D"
    }
  }
}