Explicit Homology Representation for Finite Groups Acting on Riemann Surfaces

S. Allen Broughton, Linden Disney-Hogg

Given a finite group $G$ acting orientably on a surface $S$ of genus $\ddot{I}ƒ\ge 2$, the group $G$ acts faithfully on the homology group $H_1(S;\mathbb{Z})$, preserving the symplecti…