Surface groups as subgroups of hyperbolic groups (Ex)

Let $G$$<wikitex>; Let $G$ be a torsionfree hyperbolic group which occurs as the fundamental group of an aspherical closed $-manifold. Show that $G$ contains the fundamental group of a closed orientable surface of genus $\ge 2$ as subgroup. </wikitex> [[Category:Exercises]] [[Category:Exercises without solution]]G$ be a torsionfree hyperbolic group which occurs as the fundamental group of an aspherical closed $3$$3$-manifold. Show that $G$$G$ contains the fundamental group of a closed orientable surface of genus $\ge 2$$\ge 2$ as subgroup.