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≥2), of given volume and fixed topology. The resulting entropy estimates emphasize the basic role, in simplicial quantum gravity, of the moduli spaces Hom(π1(M),G)/G associated with the representations of the fundamental group of the manifold, π1(M), into a Lie group G.

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