We reconsider Chern-Simons gauge theory on a Seifert manifold M (the total
space of a nontrivial circle bundle over a Riemann surface Σ).
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.