The Tambara-Yamagami categories and 3-manifold invariants

2010/09/09 by Vladimir Turaev, Turaev, Vladimir, Leonid Vainerman +1
Mathematics · #Category Theory (math.CT) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.CT #math.GT #math.QA

paper · pdf · doi:10.48550/arxiv.1009.1798

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

arxiv created 2011/04/13 · arxiv updated 2011/04/14

Abstract

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