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 Chern-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.

• Received 17 August 1999

DOI:https://doi.org/10.1103/PhysRevE.61.3174