  We show that the prequantum line bundle on the moduli space of flat $SU(2)$
connections on a closed Riemann surface of positive genus has degree 1. It then
follows from work of Lawton and the second author that the classifying map for
this line bundle induces a homotopy equivalence between the stable moduli space
of flat $SU(N)$ connections, in the limit as $N$ tends to infinity, and
$\mathbb{C}P^\infty$. Applications to the stable moduli space of flat unitary
connections are also discussed.
