The Tambara-Yamagami categories and 3-manifold invariants
Abstract
We prove that if two Tambara-Yamagami categories TY(A,,) and TY(A',',') give rise to the same state sum invariants of 3-manifolds and the order of one of the groups A, A' is odd, then =' and there is a group isomorphism A≈ A' carrying to '. 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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