{
  "id": "0801.3893",
  "version": "v3",
  "published": "2008-01-25T07:58:04.000Z",
  "updated": "2009-05-16T06:35:14.000Z",
  "title": "A Unified Quantum SO(3) Invariant for Rational Homology 3-Spheres",
  "authors": [
    "Anna Beliakova",
    "Irmgard Buehler",
    "Thang Le"
  ],
  "comment": "31 pages, 18 Figures; Appendix substantially revised",
  "journal": "Inventiones, Volume 185, Issue 1 (2011), Page 121-174",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "Given a rational homology 3-sphere M with the first integral homology of rank b and a link L inside M, colored by odd numbers, we construct a unified invariant I_{M,L} belonging to a modification of the Habiro ring where b is inverted. Our unified invariant dominates the whole set of the SO(3) Witten-Reshetikhin-Turaev invariants of the pair (M,L). If b=1 and L is empty, I_M coincides with Habiro's invariant of integral homology 3-spheres. For b>1, the unified invariant defined by the third author is determined by I_M. One of the applications are the new Ohtsuki series (perturbative expansions of I_M at roots of unity) dominating all quantum SO(3) invariants.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-05-16T06:35:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57N10",
      "57M25"
    ],
    "keywords": [
      "rational homology",
      "unified quantum",
      "first integral homology",
      "ohtsuki series",
      "third author"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00222-010-0304-5",
      "journal": "Inventiones Mathematicae",
      "year": 2011,
      "month": "Jul",
      "volume": 185,
      "number": 1,
      "pages": 121
    },
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011InMat.185..121B"
    }
  }
}