The commutator subgroups of free groups and surface groups
Geometric Topology
2022-07-19 v2 Group Theory
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
@article{arxiv.2101.05905,
title = {The commutator subgroups of free groups and surface groups},
author = {Andrew Putman},
journal= {arXiv preprint arXiv:2101.05905},
year = {2022}
}
Comments
20 pages, 4 figures; minor revision; to appear in Enseign. Math