  A mimetic discretization of the Abelian Chern-Simons theory is presented. The
study relies on the formulation of a theory of differential forms in the
lattice, including a consistent definition of the Hodge duality operation.
Explicit expressions for the Gauss Linking Number in the lattice, which
correspond to their continuum counterparts are given. A discussion of the
discretization of metric structures in the space of transverse vector densities
is presented. The study of these metrics could serve to obtain explicit
formulae for knot an link invariants in the lattice.
