{
  "id": "math/0211044",
  "version": "v1",
  "published": "2002-11-04T12:23:57.000Z",
  "updated": "2002-11-04T12:23:57.000Z",
  "title": "On the quantum sl_2 invariants of knots and integral homology spheres",
  "authors": [
    "Kazuo Habiro"
  ],
  "comment": "Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper5.abs.html",
  "journal": "Geom. Topol. Monogr. 4 (2002) 55-68",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "We will announce some results on the values of quantum sl_2 invariants of knots and integral homology spheres. Lawrence's universal sl_2 invariant of knots takes values in a fairly small subalgebra of the center of the h-adic version of the quantized enveloping algebra of sl_2. This implies an integrality result on the colored Jones polynomials of a knot. We define an invariant of integral homology spheres with values in a completion of the Laurent polynomial ring of one variable over the integers which specializes at roots of unity to the Witten-Reshetikhin-Turaev invariants. The definition of our invariant provides a new definition of Witten-Reshetikhin-Turaev invariant of integral homology spheres.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-11-04T12:23:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "17B37"
    ],
    "keywords": [
      "integral homology spheres",
      "witten-reshetikhin-turaev invariant",
      "definition",
      "fairly small subalgebra",
      "laurent polynomial"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....11044H"
    }
  }
}