The action of the Mapping Class Group on the fundamental group of the complement of a finite subset of a Riemann surface of positive genus

Abstract

We describe the action of the mapping class group $M(g,n)$ on the fundamental group of $T_{g,n}$, a compact orientable topological surface of positive genus $g$ with $n$ marked points. This is achieved by computing the image of the generators of $M(g,n)$ as outer automorphisms of the fundamental group.