2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72605Herein 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 $π_1(M^{[n]})\to H_1(M)$ is generated by transpositions for sufficiently large $n$. Specifically, we treat $M$ as a polyhedron, and the edge set of $M$ generates this group.9 pages, 2 figuresGroup Theory20F36 20F05text