Good morning,
I am having a hard time trying to describe the commutator subgroup of a surface group. Namely, if $S$ is a compact orientable surface and $G$ its fundamental subgroup, let's recall that $G$ is given by the following presentation $ \langle a_1, b_1, ..., a_g, b_g \ | \ \prod_{1\leq i \leq g}{[a_i,bi]} =1 \rangle$. Its commutator subgroup is an infinite rank free group. Can one give a set of generator of this subgroup ? Or even better, could one make such a set free ?
I would be grateful for any hint or reference !
Selim