Geometric discretization scheme applied to the Abelian Chern-Simons theory

We give a detailed general description of a recent geometrical discretization scheme and illustrate, by explicit numerical calculation, the scheme's ability to capture topological features. The scheme is applied to the Abelian Chem-Simons theory and leads, after a necessary field doubling, to an expression for the discrete partition function in terms of untwisted Reidemeister torsion and of various triangulation-dependent factors. The discrete partition 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 function.