A MODEL OF THREE-DIMENSIONAL LATTICE GRAVITY

Abstract

A model is proposed which generates all oriented 3D simplicial complexes weighted with an invariant associated with a topological lattice gauge theory. When the gauge group is SU q (2), q n =1, it is the Turaev-Viro invariant and the model may be regarded as a nonperturbative definition of 3D simplicial quantum gravity. If one takes a finite Abelian group G, the corresponding invariant gives the rank of the first cohomology group of a complex C:I G (C)=rank(H 1 (C,G)), which means a topological expansion in the Betti number b 1 . In general, it is a theory of the Dijkgraaf-Witten type, i.e., determined completely by the fundamental group of a manifold.