On the homology of the commutator subgroup of the pure braid group,Proceedings of the American Mathematical Society

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On the homology of the commutator subgroup of the pure braid group
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-03-29 , DOI: 10.1090/proc/15404
Andrea Bianchi

Abstract:We study the homology of $[P_{n},P_{n}]$ , the commutator subgroup of the pure braid group on

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 $\textnormal {cd}([P_{n},P_{n}])=n-2$ .

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