{
  "id": "0905.4186",
  "version": "v2",
  "published": "2009-05-26T12:26:07.000Z",
  "updated": "2011-08-05T13:48:31.000Z",
  "title": "Real algebraic knots of low degree",
  "authors": [
    "Johan Björklund"
  ],
  "comment": "28 pages",
  "doi": "10.1142/S0218216511009248",
  "categories": [
    "math.GT",
    "math.AG"
  ],
  "abstract": "In this paper we study rational real algebraic knots in $\\R P^3$. We show that two real algebraic knots of degree $\\leq5$ are rigidly isotopic if and only if their degrees and encomplexed writhes are equal. We also show that any irreducible smooth knot which admits a plane projection with less than or equal to four crossings has a rational parametrization of degree $\\leq 6$. Furthermore an explicit construction of rational knots of a given degree with arbitrary encomplexed writhe (subject to natural restrictions) is presented.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-08-05T13:48:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "low degree",
      "study rational real algebraic knots",
      "arbitrary encomplexed writhe",
      "rational knots",
      "irreducible smooth knot"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.4186B"
    }
  }
}