-dimensional topological quantum field theory from subfactors and Dehn surgery formula for 3-manifold invariants

Abstract: In this paper, we establish the general theory of -dimensional topological quantum field theory (in short, TQFT) with a Verlinde basis. It is a consequence that we have a Dehn surgery formula for 3-manifold invariants for this kind of TQFT''s. We will show that Turaev–Viro–Ocneanu unitary TQFT''s obtained from subfactors satisfy the axioms of TQFT''s with Verlinde bases. Hence, in a Turaev–Viro–Ocneanu TQFT, we have a Dehn surgery formula for 3-manifolds. It turns out that this Dehn surgery formula is nothing but the formula of the Reshetikhin–Turaev invariant constructed from a tube system, which is a modular category corresponding to the quantum double construction of a -tensor category. In Sato and Wakui (J. Knot Theory Ramif. 12 (2003) 543), we will exhibit computations of Turaev–Viro–Ocneanu invariants for several “basic 3-manifolds”. In the appendix, we discuss the relationship between the system of - bimodules arising from the asymptotic inclusion constructed from and the tube system obtained from a subfactor . [Copyright &y& Elsevier]