The commutator subgroups of free groups and surface groups
Andrew Putman
University of Notre Dame, USA
Abstract
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.
Cite this article
Andrew Putman, The commutator subgroups of free groups and surface groups. Enseign. Math. 68 (2022), no. 3/4, pp. 389–408
DOI 10.4171/LEM/1035