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We show that the partition function of the Ponzano-Regge quantum gravitymodel can be written as a sum over surfaces in a $(2+1)$ dimensionalspace-time. We suggest a geometrical meaning, in terms of surfaces, for the(regulated) divergences that appear in the partition function.Comment: latex 14 pages (10 pages of text, 4 pages of figures), 4 epsfig  figures, University of Pittsburgh preprint. No change has been made. The  previous file has been corrupte

A definition of the Ponzano–Regge quantum gravity model in terms of surfacesa)