ON THE HOMOLOGY OF THE COMMUTATOR SUBGROUP OF THE PURE BRAID GROUP

被引：1

作者：

Bianchi, Andrea ^{[1
,2
]}

机构：

[1] Univ Bonn, Math Inst, Endenicher Allee 60, Bonn, Germany

[2] Univ Copenhagen, Dept Math Sci, Univ Pk 5, Copenhagen, Denmark

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 149卷 / 06期

关键词：

Pure braid group; commutator subgroup; cohomological dimension; MILNOR FIBER; COHOMOLOGY;

D O I：

10.1090/proc/15404

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 <= l <= n - 2. As a consequence we determine the cohomological dimension of [P-n, P-n]: for n >= 2 we have cd([P-n, P-n]) = n - 2.

引用

页码：2387 / 2401

页数：15

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