{
  "id": "0803.0103",
  "version": "v1",
  "published": "2008-03-02T06:46:46.000Z",
  "updated": "2008-03-02T06:46:46.000Z",
  "title": "Meridian twisting of closed braids and the Homfly polynomial",
  "authors": [
    "Tamás Kálmán"
  ],
  "comment": "14 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $\\beta$ be a braid on $n$ strands, with exponent sum $w$. Let $\\Delta$ be the Garside half-twist braid. We prove that the coefficient of $v^{w-n+1}$ in the Homfly polynomial of the closure of $\\beta$ agrees with $(-1)^{n-1}$ times the coefficient of $v^{w+n^2-1}$ in the Homfly polynomial of the closure of $\\beta\\Delta^2$. This coincidence implies that the lower Morton--Franks-Williams estimate for the $v$--degree of the Homfly polynomial of $\\hat\\beta$ is sharp if and only if the upper MFW estimate is sharp for the $v$--degree of the Homfly polynomial of $\\hat{\\beta\\Delta^2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-02T06:46:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "homfly polynomial",
      "closed braids",
      "meridian twisting",
      "upper mfw estimate",
      "garside half-twist braid"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1017/S0305004108002016",
      "journal": "Mathematical Proceedings of the Cambridge Philosophical Society",
      "year": 2008,
      "month": "Oct",
      "volume": 146,
      "number": 3,
      "pages": 649
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008MPCPS.146..649K"
    }
  }
}