Exterior differentiation in the Reg . e calculus

Regge manifolds are piecewise continuous manifolds constructed from a finite nutnber of basic building blocks. On such manifolds piecewise continuous forms can be defined in a way similar to differential forms on a differentiable manifold. Regge manifolds are used extensively in the construction ofspace-times in numerical general relativity. In this paper a definition ofexterior differentiation suitable for use on piecewise continuous forms on a Regge manifold is presented. It is shown that this definition leads to a version ofStokes' theorem and also to the usual result that d 2 = O. This is preceded by a discussion ofcertain geometrical properties ofthe Regge manifolds. It is shown that the version ofStokes' theorem presented here coincides with the usual definition when the Regge manifold is refined, by increasing the number of cells while keeping the total volume constant, to a smooth manifold.