On a class of topological quantum field theories in three-dimensions

We investigate the Chung-Fukuma-Shapere theory, or Kuperberg theory, of threedimensional lattice topological field theory. We construct a functor which satisfies the Atiyah’s axioms of topological quantum field theory by reformulating the theory as Turaev-Viro type state-sum theory on a triangulated manifold. The theory can also be extended to give a topological invariant of manifolds with boundary. ∗E-mail address: [email protected]