The Tambara-Yamagami categories and 3-manifold invariants

Details The Tambara-Yamagami categories and 3-manifold invariants The Tambara-Yamagami categories and 3-manifold invariants

2010-09-09

arxiv.org/abs/1009.1798v2

Mathematics

Quantum Algebra

10 pages. In the second version the introduction has been considerably extended and the references updated

Scientific paper

We prove that if two Tambara-Yamagami categories TY(A,\chi,\nu) and 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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