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

Andrea Bianchi
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引用次数: 1

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 $\mathrm{cd}([P_n,P_n])=n-2$.
纯辫群的交换子群的同调性
研究了$n$链上纯辫群的交换子群$[P_n,P_n]$的同调性,证明了$H_l([P_n,P_n])$包含一个对所有$1\leq l\leq n-2$的无限秩的自由阿贝尔群。因此,我们确定$[P_n,P_n]$的上同调维数:对于$n\geq 2$,我们有$\mathrm{cd}([P_n,P_n])=n-2$。
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