The Construction of Sorkin Triangulations

Some time ago, Sorkin (1975) reported investigations of the time evolution and initial value problems in Regge calculus, for one triangulation each of the manifolds $R\ast S^3$ and $R^4$. Here we display the simple, local characteristic of those triangulations which underlies the structure found by Sorkin, and emphasise its general applicability, and therefore the general validity of Sorkin’s conclusions. We also make some elementary observations on the resulting structure of the time evolution and initial value problems in Regge calculus, and add some comments and speculations.