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.
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页码：2387 / 2401
页数：15
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