2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115081We prove that if $\F$ is an abelian group of $C^1$ diffeomorphisms isotopic to the identity of a closed surface $S$ of genus at least two then there is a common fixed point for all elements of $\F.$Dynamical Systems37E30; 37C25text