{
  "id": "math/0610484",
  "version": "v1",
  "published": "2006-10-16T13:17:40.000Z",
  "updated": "2006-10-16T13:17:40.000Z",
  "title": "Quaternionic Invariants of Virtual Knots and Links",
  "authors": [
    "Andrew Bartholomew",
    "Roger Fenn"
  ],
  "comment": "21 pages, 13 figures, accepted by JKTR",
  "categories": [
    "math.GT",
    "math.RA"
  ],
  "abstract": "In this paper we define and give examples of a family of polynomial invariants of virtual knots and links. They arise by considering certain 2$\\times$2 matrices with entries in a possibly non-commutative ring, for example the quaternions. These polynomials are sufficiently powerful to distinguish the Kishino knot from any classical knot, including the unknot.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-16T13:17:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "virtual knots",
      "quaternionic invariants",
      "polynomial invariants",
      "kishino knot"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10484B"
    }
  }
}