  We investigate the Chung-Fukuma-Shapere theory, or Kuperberg theory, of
three-dimensional 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.
