Singular Vertices and the Triangulation Space of the D-sphere

Details Singular Vertices and the Triangulation Space of the D-sphere Singular Vertices and the Triangulation Space of the D-sphere

1995-12-07

arxiv.org/abs/hep-lat/9512012v1

Nucl.Phys. B468 (1996) 263-276

Physics

High Energy Physics

High Energy Physics - Lattice

15 pages, 9 figures

Scientific paper

10.1016/0550-3213(96)00130-7

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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