  In a previous paper [\AS], we used superspace techniques to prove that
perturbation theory (around a classical solution with no zero modes) for
Chern--Simons quantum field theory on a general $3$-manifold $M$ is finite. We
conjectured (and proved for the case of $2$-loops) that, after adding
counterterms of the expected form, the terms in the perturbation theory define
topological invariants. In this paper we prove this conjecture. Our proof uses
a geometric compactification of the region on which the Feynman integrand of
Feynman diagrams is smooth as well as an extension of the basic propagator of
the theory.
