Abstract
The authors exploit the coarse classification of Riemannian geometries provided by Gromov's pre-compactness theorem (1981) in order to give a rigorous characterization of the partition function of n-dimensional, (n>or=2), lattice quantum gravity. They prove that the resulting theory admits a continuum limit describing phase transitions between different homotopy types of manifolds, with phases parametrized by the fundamental group and by the (Whitehead) torsions of the manifolds sampled. They also show that the results obtained coincide, when specialized to dimension two, with those of two-dimensional quantum gravity models based on random triangulations of surfaces.
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