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

Andrea Bianchi

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arXiv · 1905.05099

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

Andrea Bianchi

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Abstract

We study the homology of $[P_n,P_n]$, the commutator subgroup of the pure braid group on $n$ strands, and show that $H_l([P_n,P_n])$ contains a free abelian group of infinite rank for all $1\leq l\leq n-2$. As a consequence we determine the cohomological dimension of $[P_n,P_n]$: for $n\geq 2$ we have $\mathrm{cd}([P_n,P_n])=n-2$.

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Andrea Bianchi. 2019-05-13. On the homology of the commutator subgroup of the pure braid group. https://arxiv.org/abs/1905.05099

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