Speaker
Bruno Benedetti
(TU Berlin)
Description
In 1995 Durhuus and Jonsson introduced the class of
locally constructible (LC) triangulations and showed
that there are at most exponentially many LC 3-
spheres with N tetrahedra. Such upper bounds are
crucial for the convergence of the dynamical
triangulations model in discrete quantum
gravity. We show that any simply connected manifold of
dimension different than four admits an LC
triangulation. However, plenty of non-LC d-spheres exist
for each d>2. Also, we show how discrete Morse
theory yields exponential cutoffs for the class of all
triangulations of manifolds with N facets.
