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The commutator subgroups of free groups and surface groups

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 نشر من قبل Andrew Putman
 تاريخ النشر 2021
  مجال البحث
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 تأليف Andrew Putman




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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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