{
  "id": "1505.06666",
  "version": "v1",
  "published": "2015-05-25T15:43:29.000Z",
  "updated": "2015-05-25T15:43:29.000Z",
  "title": "Identifying the invariants for classical knots and links from the Yokonuma-Hecke algebras",
  "authors": [
    "Maria Chlouveraki",
    "Jesus Juyumaya",
    "Konstantinos Karvounis",
    "Sofia Lambropoulou"
  ],
  "comment": "44 pages, 11 figures, 1 table. For related computational packages, see http://math.ntua.gr/~sofia/yokonuma",
  "categories": [
    "math.GT",
    "math.RT"
  ],
  "abstract": "In this paper we study the Juyumaya-Lambropoulou invariants $\\Delta_{d,D}$ for classical knots and links constructed from the Yokonuma-Hecke algebras, and in particular their relationship to the Homflypt polynomial. We first prove that the Markov trace ${\\rm tr}_{d,D}$ on the Yokonuma-Hecke algebras can be computed on classical knots and links by five rules which do not involve the framing generators. Using this we show that the invariants $\\Delta_{d,D}$ on classical knots are topologically equivalent to the Homflypt polynomial. We further describe the behaviour of the invariants $\\Delta_{d,D}$ on arbitrary links in relation to the Homflypt polynomial by means of a closed formula. Finally, we show that the invariants $\\Delta_{d,D}$ are not topologically equivalent to the Homflypt polynomial by providing computational data for six pairs of Homflypt-equivalent links which are distinguished by $\\Delta_{d,D}$ and a diagrammatic proof for one of these pairs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-25T15:43:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M25",
      "20F36",
      "20F38",
      "20C08"
    ],
    "keywords": [
      "classical knots",
      "yokonuma-hecke algebras",
      "homflypt polynomial",
      "topologically equivalent",
      "markov trace"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150506666C"
    }
  }
}