  We study Chern-Simons theory on 3-manifolds $M$ that are circle-bundles over
2-dimensional surfaces $\Sigma$ and show that the method of Abelianisation,
previously employed for trivial bundles $\Sigma \times S^1$, can be adapted to
this case. This reduces the non-Abelian theory on $M$ to a 2-dimensional
Abelian theory on $\Sigma$ which we identify with q-deformed Yang-Mills theory,
as anticipated by Vafa et al. We compare and contrast our results with those
obtained by Beasley and Witten using the method of non-Abelian localisation,
and determine the surgery and framing presecription implicit in this path
integral evaluation. We also comment on the extension of these methods to BF
theory and other generalisations.

High Energy Physics - Theory