A Special Subgroup of the Surface Braid Group

Abstract

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.

9 pages, 2 figures

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