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

共 19 条

[1]

Arnold VI., 1969, MAT ZAMETKI, V5, P227

[2]

Artin E, 1925, Abh Aus Dem Math Semin Universitat Hambg, V4, P47, DOI [DOI 10.1007/BF02950718, 10.1007/BF02980599, DOI 10.1007/BF02980599]

[3] Topological complexity of unordered configuration spaces of surfaces [J].

Bianchi, Andrea ;

Recio-Mitter, David .

ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2019, 19 (03) :1359-1384

[4] Cohomology of affine Artin groups and applications [J].

Callegaro, Filippo ;

Moroni, Davide ;

Salvetti, Mario .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 360 (08) :4169-4188

[5] The homology of the Milnor fiber for classical braid groups [J].

Callegaro, Filippo .

ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2006, 6 :1903-1923

[6] Arithmetic properties of the cohomology of braid groups [J].

De Concini, C ;

Procesi, C ;

Salvetti, M .

TOPOLOGY, 2001, 40 (04) :739-751

[7]

DECONCINI C, 1999, ANN SCUOLA NORM SUP, V28, P695

[8] The Orlik-Solomon complex and Milnor fibre homology [J].

Denham, G .

TOPOLOGY AND ITS APPLICATIONS, 2002, 118 (1-2) :45-63

[9]

Djawadi D., 2009, THESIS

[10]

FADELL E, 1962, MATH SCAND, V10, DOI DOI 10.7146/MATH.SCAND.A-10517

← 1 2 →