  Simplicial versions of topological abelian gauge theories are constructed
which reproduce the continuum expressions for the partition function and Wilson
expectation value of linked loops, expressible in terms of R-torsion and
linking numbers respectively. The new feature which makes this possible is the
introduction of simplicial fields (cochains) associated with the dual
triangulation of the background manifold, as well as with the triangulation
itself. This doubling of fields, reminiscent of lattice fermion doubling, is
required because the natural simplicial analogue of the Hodge star operator
maps between cochains of a triangulation and cochains of the dual
triangulation. The simplicial analogue of Hodge-de Rham theory is developed,
along with a natural simplicial framework for considering linking numbers of
framed loops. When the loops represent torsion elements of the homology of the
manifold then Q/Z-valued torsion pairings appear in place of linking numbers
for certain discrete values of the coupling parameter of the theory.
