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.
Bianchi, A. (2021). On the homology of the commutator subgroup of the pure braid group. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 149(6), 2387-2401 [10.1090/proc/15404].
On the homology of the commutator subgroup of the pure braid group
Bianchi, Andrea
2021
Abstract
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.File in questo prodotto:
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