  Herein we prove that if $M$ is a compact oriented Riemann surface of genus
$g$, and $M^{[n]}$ is the classifying space of $n$ distinct, unordered points
on $M$, then the kernel of the map $\pi_1(M^{[n]})\to H_1(M)$ is generated by
transpositions for sufficiently large $n$. Specifically, we treat $M$ as a
polyhedron, and the edge set of $M$ generates this group.
