(2+1)-dimensional topological quantum field theory with a Verlinde basis and Turaev-Viro-Ocneanu invariants of 3-manifolds

In this article, we discuss a (2+1)-dimensional topological quantum field theory, for short TQFT, with a Verlinde basis. As a conclusion of this general theory, we have a Dehn surgery formula. We show that Turaev-Viro-Ocneanu TQFT has a Verlinde basis. Several applications of this theorem are exposed. Based on Izumi’s data of subfactors, we list several computations of Turaev-Viro-Ocneanu invariants for some 3-manifolds.