We prove that if two Tambara-Yamagami categories and~ give rise to the same state sum invariants of 3-manifolds and the order of one of the groups~ is odd, then~ and there is a group isomorphism~ carrying~ to~. The proof is based on an explicit computation of the state sum invariants for the lens spaces of type~.
Cite this article
Vladimir Turaev, Leonid Vainerman, The Tambara-Yamagami categories and 3-manifold invariants. Enseign. Math. 58 (2012), no. 1/2, pp. 131–146DOI 10.4171/LEM/58-1-6