3-DIMENSIONAL GRAVITY FROM THE TURAEV-VIRO INVARIANT

We study the q-deformed su(2) spin network as a three-dimensional quantum gravity model. We show that in the semiclassical continuum limit the Turaev-Viro invariant obtained recently defines a naturally regularized path integral a la Ponzano and Regge, in which a contribution from the cosmological term is effectively included. The regularization-dependent cosmological constant is found to be 4-pi2/k2+O(k-4), where q2k = 1. We also discuss the relation to the Euclidean Chern-Simons-Witten gravity in three dimensions.