The Tambara-Yamagami categories and 3-manifold invariants (Q353416)
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scientific article; zbMATH DE number 6187660
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Tambara-Yamagami categories and 3-manifold invariants |
scientific article; zbMATH DE number 6187660 |
Statements
The Tambara-Yamagami categories and 3-manifold invariants (English)
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12 July 2013
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Summary: 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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