The Tambara-Yamagami categories and 3-manifold invariants
Quantum Algebra
2011-04-14 v2 Category Theory
Geometric Topology
Abstract
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).
Keywords
Cite
@article{arxiv.1009.1798,
title = {The Tambara-Yamagami categories and 3-manifold invariants},
author = {Vladimir Turaev and Leonid Vainerman},
journal= {arXiv preprint arXiv:1009.1798},
year = {2011}
}
Comments
10 pages. In the second version the introduction has been considerably extended and the references updated