v 1 1 6 A pr 1 99 2 INTERSECTION FORMS AND THE GEOMETRY OF LATTICE CHERN - SIMONS THEORY

We show that it is possible to formulate Abelian Chern-Simons theory on a lattice as a topological field theory. We discuss the relationship between gauge invariance of the Chern-Simons lattice action and the topological interpretation of the canonical structure. We show that these theories are exactly solvable and have the same degrees of freedom as the analogous continuum theories. In the continuum, Chern-Simons theory [1,2] is a topological field theory [3,4]. It is exactly solvable and is related to interesting topological structures such as the Witten invariants of three-manifolds and the Jones polynomial and other knot invariants for links embedded in three-manifolds. Its canonical formalism also has an interesting relationship with conformal field theory in two dimensions. As a model for physical phenomena its U(1)