  Previous path integral treatments of Yang-Mills on a Riemann surface
automatically sum over principal fiber bundles of all possible topological
types in computing quantum expectations. This paper extends the path integral
formulation to treat separately each topological sector. The formulation is
sufficiently explicit to calculate Wilson line expectations exactly. Further,
it suggests two new measures on the moduli space of flat connections, one of
which proves to agree with the small-volume limit of the Yang-Mills measure.
\copyright {\em 1996 American Institute of Physics.}
