LATTICE TOPOLOGICAL FIELD-THEORY IN 2 DIMENSIONS

The lattice definition of a two-dimensional topological field theory ( TFT) is given generically, and the exact solution is obtained explicit ly. In particular, the set of all lattice topological field theories i s shown to be in one-to-one correspondence with the set of all associa tive algebras R, and the physical Hilbert space is identified with the center Z(R) of the associative algebra R. Perturbations of TFT's are also considered in this approach, showing that the form of topological perturbations is automatically determined, and that all TFT's are obt ained from one TFT by such perturbations. Several examples are present ed, including twisted N = 2 minimal topological matter and the case wh ere R is a group ring.