Singular Vertices and the Triangulation Space of the D-sphere
Abstract
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.
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