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L’Enseignement Mathématique


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Volume 58, Issue 1/2, 2012, pp. 131–146
DOI: 10.4171/LEM/58-1-6

Published online: 2012-06-30

The Tambara-Yamagami categories and 3-manifold invariants

Vladimir Turaev[1] and Leonid Vainerman[2]

(1) Indiana University, Bloomington, USA
(2) Université de Caen, France

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

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Turaev Vladimir, Vainerman Leonid: The Tambara-Yamagami categories and 3-manifold invariants. Enseign. Math. 58 (2012), 131-146. doi: 10.4171/LEM/58-1-6