  The moduli space of flat SU(2) connections on a punctured surface, having
prescribed holonomy around the punctures, is a compact smooth manifold if the
prescription is generic. This paper gives a direct, elementary proof that the
trace of the holonomy around a certain loop determines a Bott-Morse function on
the moduli space which is perfect, meaning that the Morse inequalities are
equalities. This leads to an attractive recursion for the Betti numbers of the
moduli space, which agrees with the Harder-Narasimhan formula in the case of
one puncture with holonomy -1.
