{
  "id": "0803.0754",
  "version": "v3",
  "published": "2008-03-05T22:27:00.000Z",
  "updated": "2008-04-03T14:41:45.000Z",
  "title": "A Sequence of Degree One Vassiliev Invariants for Virtual Knots",
  "authors": [
    "Allison Henrich"
  ],
  "comment": "26 pages, 19 figures, modified example and updated references",
  "journal": "Journal of Knot Theory and its Ramifications 19, 4 (2010), pp. 461--487",
  "doi": "10.1142/10.1142/S0218216510007917",
  "categories": [
    "math.GT"
  ],
  "abstract": "For ordinary knots in R3, there are no degree one Vassiliev invariants. For virtual knots, however, the space of degree one Vassiliev invariants is infinite dimensional. We introduce a sequence of three degree one Vassiliev invariants of virtual knots of increasing strength. We demonstrate that the strongest invariant is a universal Vassiliev invariant of degree one for virtual knots in the sense that any other degree one Vassiliev invariant can be recovered from it by a certain natural construction. To prove these results, we extend the based matrix invariant introduced by Turaev for virtual strings to the class of singular virtual knots with one double-point.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-04-03T14:41:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "universal vassiliev invariant",
      "singular virtual knots",
      "strongest invariant",
      "infinite dimensional",
      "ordinary knots"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.0754H"
    }
  }
}