Computations of Turaev-Viro-Ocneanu invariants of 3-manifolds from subfactors

Details Computations of Turaev-Viro-Ocneanu invariants of 3-manifolds from subfactors Computations of Turaev-Viro-Ocneanu invariants of 3-manifolds from subfactors

2002-08-30

arxiv.org/abs/math/0208242v1

Mathematics

Operator Algebras

32 pages, 20 figures

Scientific paper

In this paper, we establish a rigorous correspondence between the two tube algebras, that one comes from the Turaev-Viro-Ocneanu TQFT introduced by Ocneanu and another comes from the sector theory introduced by Izumi, and construct a canonical isomorphism between the centers of the two tube algebras, which is a conjugate linear isomorphism preserving the products of the two algebras and commuting with the actions of SL(2,Z). Via this correspondence and the Dehn surgery formula, we compute Turaev-Viro-Ocneanu invariants from several subfactors for basic 3-manifolds including lens spaces and Brieskorn 3-manifolds by using Izumi's data written in terms of sectors.

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