STRUCTURE OF TOPOLOGICAL LATTICE FIELD-THEORIES IN 3 DIMENSIONS

We construct and classify topological lattice field theories in three dimensions. After defining a general class of local lattice field theories, we impose invariance under arbitrary topology-preserving deformations of the underlying lattice, which are generated by two new local lattice moves. Invariant solutions are in one-to-one correspondence with Hopf algebras satisfying a certain constraint. As an example, we study in detail the topological lattice field theory corresponding to the Hopf algebra based on the group ring C[G], and show that it is equivalent to lattice gauge theory at zero coupling, and to the Ponzano-Regge theory for G = SU(2).