{
  "id": "math/0703786",
  "version": "v1",
  "published": "2007-03-27T07:47:46.000Z",
  "updated": "2007-03-27T07:47:46.000Z",
  "title": "Gordian distance and Vassiliev invariants",
  "authors": [
    "Sebastian Baader"
  ],
  "comment": "7 pages, 8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "The Gordian distance between two knots measures how many crossing changes are needed to transform one knot into the other. It is known that there are always infinitely many non-equivalent knots `between' a pair of knots of Gordian distance two. In this paper we prove an extreme generalisation of this fact: there are knots with arbitrarily prescribed Vassiliev invariants between every pair of knots of Gordian distance two.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-27T07:47:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "gordian distance",
      "arbitrarily prescribed vassiliev invariants",
      "extreme generalisation",
      "non-equivalent knots",
      "knots measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3786B"
    }
  }
}