The commutator subgroups of free groups and surface groups

  • Andrew Putman

    University of Notre Dame, USA
The commutator subgroups of free groups and surface groups cover

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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