{
  "id": "1002.1803",
  "version": "v2",
  "published": "2010-02-09T09:15:23.000Z",
  "updated": "2011-06-06T15:38:04.000Z",
  "title": "Milnor invariants and the HOMFLYPT polynomial",
  "authors": [
    "Jean-Baptiste Meilhan",
    "Akira Yasuhara"
  ],
  "comment": "Entirely revised version (20 pages). The main result was generalized and extended to Milnor invariants of links, using new arguments. Several corollaries are given, in particular one containing the main result of the previous version. Example and References added",
  "journal": "Geom.Topol. 16 (2012) 889-917",
  "categories": [
    "math.GT"
  ],
  "abstract": "We give formulas expressing Milnor invariants of an n-component link L in the 3-sphere in terms of the HOMFLYPT polynomial as follows. If the Milnor invariant \\bar{\\mu}_J(L) vanishes for any sequence J with length at most k, then any Milnor \\bar{\\mu}-invariant \\bar{\\mu}_I(L) with length between 3 and 2k+1 can be represented as a combination of HOMFLYPT polynomial of knots obtained from the link by certain band sum operations. In particular, the `first non vanishing' Milnor invariants can be always represented as such a linear combination.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-06-06T15:38:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27"
    ],
    "keywords": [
      "homflypt polynomial",
      "formulas expressing milnor invariants",
      "band sum operations",
      "first non",
      "n-component link"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.1803M"
    }
  }
}