HOLONOMY AND ENTROPY ESTIMATES FOR DYNAMICALLY TRIANGULATED MANIFOLDS

We provide an elementary proof of the exponential bound to the number of distinct dynamical triangulations of an n-dimensional manifold M (n greater than or equal to 2), of given volume and fixed topology. The resulting entropy estimates emphasize the basic role, in simplicial quantum gravity, of the moduli spaces H o m(pi(1)(M),G)/G associated with the representations of the fundamental group of the manifold, pi(1)(M), into a Lie group G. (C) 1995 American Institute of Physics.