  It is well known that one can parameterize 2-D Riemannian structures by
conformal transformations and diffeomorphisms of fiducial constant curvature
geometries; and that this construction has a natural setting in general
relativity theory in 2-D. I will show that a similar parameterization exists
for 3-D Riemannian structures, with the conformal transformations and
diffeomorphisms of the 2-D case replaced by a finite dimensional group of gauge
transformations. This parameterization emerges from the theory of 3-D gravity
coupled to topological matter.
