Computations of Turaev-viro-ocneanu Invariants of 3-manifolds from Subfactors

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.