  I argue that the complete partition function of 3D quantum gravity is given
by a path integral over gauge-inequivalent manifolds times the Chern-Simons
partition function. In a discrete version, it gives a sum over simplicial
complexes weighted with the Turaev-Viro invariant. Then, I discuss how this
invariant can be included in the general framework of lattice gauge theory
(qQCD$_3$). To make sense of it, one needs a quantum analog of the Peter-Weyl
theorem and an invariant measure, which are introduced explicitly. The
consideration here is limited to the simplest and most interesting case of
$SL_q(2)$, $q=e^{i\frac{2\pi}{k+2}}$. At the end, I dwell on 3D generalizations
of matrix models.
