On the homology of the commutator subgroup of the pure braid group

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We study the homology of [Pn,Pn], the commutator subgroup of the pure braid group on n strands, and show that Hl([Pn,Pn]) contains a free abelian group of infinite rank for all 1≤l≤n−2. As a consequence we determine the cohomological dimension of [Pn,Pn]: for n≥2 we have cd([Pn,Pn])=n−2.
Original languageEnglish
JournalProceedings of the American Mathematical Society
Volume149
Issue number6
Pages (from-to)2387-2401
ISSN0002-9939
DOIs
Publication statusPublished - Jun 2021
Externally publishedYes

ID: 259424537