  We reconsider Chern-Simons gauge theory on a Seifert manifold M (the total
space of a nontrivial circle bundle over a Riemann surface). When M is a
Seifert manifold, Lawrence and Rozansky have shown from the exact solution of
Chern-Simons theory that the partition function has a remarkably simple
structure and can be rewritten entirely as a sum of local contributions from
the flat connections on M. We explain how this empirical fact follows from the
technique of non-abelian localization as applied to the Chern-Simons path
integral. In the process, we show that the partition function of Chern-Simons
theory on M admits a topological interpretation in terms of the equivariant
cohomology of the moduli space of flat connections on M.
