{
  "id": "1505.06667",
  "version": "v1",
  "published": "2015-05-25T15:44:38.000Z",
  "updated": "2015-05-25T15:44:38.000Z",
  "title": "On the knot invariants from the Yokonuma-Hecke algebras",
  "authors": [
    "Sergei Chmutov",
    "Slavik Jablan",
    "Konstantinos Karvounis",
    "Sofia Lambropoulou"
  ],
  "comment": "22 pages, 2 figures, 3 tables. For related computational packages see http://math.ntua.gr/~sofia/yokonuma",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper we study properties of the Juyumaya trace ${\\rm tr}_d$ and the specialized trace ${\\rm tr}_{d,D}$ on the Yokonuma-Hecke algebras; namely behaviour under inversion of a word, connected sums and mirror imaging. We then review the Juyumaya-Lambropoulou invariants for framed, classical and singular links constructed through the trace ${\\rm tr}_{d,D}$ and we also construct invariants for transverse links through the trace ${\\rm tr}_d$. In order to compare the invariants for classical links with the Homflypt polynomial we develop computer programs and we evaluate them on several pairs of knots and links which are Homflypt-equivalent. Our computations lead to our conjecture that these invariants are topologically equivalent to the Homflypt polynomial on knots. However, they do not demonstrate the same behaviour on links.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-25T15:44:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M25",
      "20F36",
      "20F38",
      "20C08"
    ],
    "keywords": [
      "yokonuma-hecke algebras",
      "knot invariants",
      "homflypt polynomial",
      "singular links",
      "juyumaya trace"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150506667C"
    }
  }
}