{
  "id": "math/0508220",
  "version": "v2",
  "published": "2005-08-12T17:36:07.000Z",
  "updated": "2006-02-06T12:35:11.000Z",
  "title": "A TQFT associated to the LMO invariant of three-dimensional manifolds",
  "authors": [
    "Dorin Cheptea",
    "Thang T Q Le"
  ],
  "comment": "28 pages, 13 postscript figures. Version 2 (Section 1 has been considerably shorten, and section 3 has been slightly shorten, since they will constitute a separate paper. Section 4, which contained only announce of results, has been suprimated; it will appear in detail elsewhere. Consequently some statements have been re-numbered. No mathematical changes have been made.)",
  "journal": "Commun.Math.Phys.272:601-634,2007",
  "doi": "10.1007/s00220-007-0241-3",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "We construct a Topological Quantum Field Theory (in the sense of Atiyah) associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from the category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category. It is built together with its truncations with respect to a natural grading, and we prove that these TQFTs are non-degenerate and anomaly-free. The TQFT(s) induce(s) a (series of) representation(s) of a subgroup ${\\cal L}_g$ of the Mapping Class Group that contains the Torelli group. The N=1 truncation produces a TQFT for the Casson-Walker-Lescop invariant.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-02-06T12:35:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57R56",
      "81T45",
      "81Q30",
      "81R50"
    ],
    "keywords": [
      "three-dimensional manifolds",
      "lmo invariant",
      "topological quantum field theory",
      "universal finite-type invariant"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Communications in Mathematical Physics",
      "year": 2007,
      "month": "Jun",
      "volume": 272,
      "number": 3,
      "pages": 601
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 689916,
      "adsabs": "2007CMaPh.272..601C"
    }
  }
}