  A beautifully simple free generating set for the commutator subgroup of a
free group was constructed by Tomaszewski. We give a new geometric proof of his
theorem, and show how to give a similar free generating set for the commutator
subgroup of a surface group. We also give a simple representation-theoretic
description of the structure of the abelianizations of these commutator
subgroups and calculate their homology.
