HOMOLOGY IN ABELIAN LATTICE MODELS

We study Abelian lattice gauge theory defined on a simplicial complex with arbitrary topology. The use of dual objects allows one to reformu late the theory in terms of different dynamical variables; however, we avoid entirely the use of the dual cell complex. Topological modes wh ich are present in the transformation now appear as homology classes, in contrast to the cohomology modes found in the dual cell picture. ir regularities of dual cell complexes do not arise in this approach. We treat the two and three-dimensional cases in detail, and prove a gener al vanishing theorem for Wilson line correlators.