EXACT 3-DIMENSIONAL LATTICE GRAVITIES

It is shown that the three-dimensional lattice theory defined by Ponzano and Regge is equivalent to the ISO(3) Chern-Simons gauge theory, which is a three-dimensional quantum gravity with Euclidean signature and a zero cosmological constant. And its regularized version defined by Turaev and Viro, which is the q-analogue of the Ponzano-Regge model, is suggested to be equivalent to the SO(4) Chern-Simons gauge theory, which is a three-dimensional quantum gravity with Euclidean signature and a cosmological constant proportional to 1/k2, where q=e2pii/(k+2).