JournalslemVol. 58, No. 1/2pp. 131–146

The Tambara-Yamagami categories and 3-manifold invariants

  • Vladimir Turaev

    Indiana University, Bloomington, USA
  • Leonid Vainerman

    Université de Caen, France
The Tambara-Yamagami categories and 3-manifold invariants cover
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Abstract

We prove that if two Tambara-Yamagami categories TY(A,χ,ν)\mathcal{TY}(A,\chi,\nu) and~TY(A,χ,ν)\mathcal{TY}(A',\chi',\nu') give rise to the same state sum invariants of 3-manifolds and the order of one of the groups~A,AA, A' is odd, then~ν=ν\nu=\nu' and there is a group isomorphism~AAA\approx A' carrying~χ\chi to~χ\chi'. The proof is based on an explicit computation of the state sum invariants for the lens spaces of type~(k,1)(k,1).

Cite this article

Vladimir Turaev, Leonid Vainerman, The Tambara-Yamagami categories and 3-manifold invariants. Enseign. Math. 58 (2012), no. 1, pp. 131–146

DOI 10.4171/LEM/58-1-6