自由群和平面群的换易子群

L’Enseignement Mathématique Pub Date : 2021-01-14 DOI:10.4171/lem/1035

Andrew Putman

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引用次数: 2

摘要

托马舍夫斯基构造了自由群的换向子群的一个漂亮简单的自由发电集。给出了他的定理的一个新的几何证明，并给出了如何给出曲面群的换易子群的一个类似的自由生集。对这些对易子子群的阿贝尔化结构给出了简单的表示理论描述，并计算了它们的同调性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The commutator subgroups of free groups and surface groups

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.

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L’Enseignement Mathématique

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