The Fundamental Group of a Compact Riemann Surface via Branched Covers

Meirav Amram, Michael Chitayat, Yaacov Kopeliovich

Let $X$ be a compact Riemann surface of genus $g$ and let $x\in X$. We derive the classical presentation of $\ddot{I}{€}_1(X,x)$ (i.e the one given by $2g$ generators $a_1,b_1, \dots, a_g,…