Singular vertices and the triangulation space of the D-sphere Original Research Article

By a sequence of numerical experiments we demonstrate that generic triangulations of the D-sphere for D > 3 contain one singular (D - 3)-simplex. The mean number of elementary D-simplices sharing this simplex increases with the volume of the triangulation according to a simple power law. The lower dimension subsimplices associated with this (D - 3)-simplex also show a singular behaviour. Possible consequences for the DT model of four-dimensional quantum gravity are discussed.