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

@article{Bianchi2019OnTH, title={On the homology of the commutator subgroup of the pure braid group}, author={Andrea Bianchi}, journal={arXiv: Algebraic Topology}, year={2019} }

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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