Papers
Authors
Leo Brewin
Abstract
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 of Stokes' 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.
Reference