NPAC Technical Report SCCS-769

Singular Vertices and the Triangulation Space of the D-Sphere

Simon Catterall, Gudmar Thorleifsson, John Kogut, Ray Renken

Submitted April 10 1996


Abstract

By a sequence of numerical experiments we demonstrate that generic triangulations of the $D-$sphere for $D>3$ contain one {\it 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.


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