A MODEL OF THREE-DIMENSIONAL LATTICE GRAVITY

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), qⁿ=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(H¹(C,G)), which means a topological expansion in the Betti number b¹. In general, it is a theory of the Dijkgraaf-Witten type, i.e., determined completely by the fundamental group of a manifold.