Geometric discretization scheme applied to the Abelian Chern-Simons theory

We give a detailed general description of a recent geometrical discretizati on scheme and illustrate, by explicit numerical calculation, the scheme's a bility to capture topological features. The scheme is applied to the Abelia n Chem-Simons theory and leads, after a necessary field doubling, to an exp ression for the discrete partition function in terms of untwisted Reidemeis ter torsion and of various triangulation-dependent factors. The discrete pa rtition function is evaluated computationally for various triangulations of S-3 and of lens spaces. The results confirm that the discretization scheme is triangulation independent and coincides with the continuum partition fu nction.