  A class of lattice gauge theories is presented which exhibits novel
topological properties. The construction is in terms of compact Wilson
variables defined on a simplicial complex which models a four dimensional
manifold with boundary. The case of Z2 and Z3 gauge groups is considered in
detail, and we prove that at certain discrete values of the coupling parameter,
the partition function in these models remains invariant under subdivision of
the underlying simplicial complex. A variety of extensions is also presented.
