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.