Homology computations for complex braid groups II

被引：2

作者：

Marin, Ivan ^{[1
]}

机构：

[1] Univ Picardie Jules Verne, LAMFA, Amiens, France

来源：

JOURNAL OF ALGEBRA | 2017年 / 477卷

关键词：

Complex reflection groups; Braid groups; Homology; ARTIN GROUPS; MILNOR FIBER; COHOMOLOGY;

D O I：

10.1016/j.jalgebra.2017.01.044

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We complete the computation of the integral homology of the generalized braid group B associated to an arbitrary irreducible complex reflection group W of exceptional type. In order to do this we explicitly computed the recursively-defined differential of a resolution of Z as a ZB-module, using parallel computing. We also deduce from this general computation the rational homology of the Milnor fiber of the singularity attached to most of these reflection groups. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：540 / 547

页数：8

共 50 条

[21] Explicit presentations for exceptional braid groups
Bessis, D
Michel, J
EXPERIMENTAL MATHEMATICS, 2004, 13 (03) : 257 - 266
[22] A journey through loop braid groups
Damiani, Celeste
EXPOSITIONES MATHEMATICAE, 2017, 35 (03) : 252 - 285
[23] The BNS invariants of the braid groups and pure braid groups of some surfaces
de Miranda e Pereiro, Carolina
Sgobbi, Wagner Carvalho
COMMUNICATIONS IN ALGEBRA, 2025, 53 (04) : 1688 - 1712
[24] Affine braid groups: a better platform than braid groups for cryptology?
Zhu, Ping
Wen, Qiaoyan
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2011, 22 (5-6) : 375 - 391
[25] The K(π, 1)-conjecture for the affine braid groups
Charney, R
Peifer, D
COMMENTARII MATHEMATICI HELVETICI, 2003, 78 (03) : 584 - 600
[26] INTERVAL GARSIDE STRUCTURES FOR THE COMPLEX BRAID GROUPS B(e, e, n)
Neaime, Georges
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 372 (12) : 8815 - 8848
[27] Generalization of the Dehornoy–Lafont Order Complex to Categories: Application to Exceptional Braid Groups
Owen Garnier
Applied Categorical Structures, 2024, 32
[28] On braid groups, homotopy groups, and modular forms
Cohen, FR
Advances in Topological Quantum Field Theory, 2004, 179 : 275 - 288
[29] On some groups related to the Braid Groups of type A
Barad, Gefry
ANNALS OF THE UNIVERSITY OF CRAIOVA-MATHEMATICS AND COMPUTER SCIENCE SERIES, 2010, 37 (02): : 47 - 61
[30] From braid groups to mapping class groups
Chen, Lei
Mukherjea, Aru
MATHEMATISCHE ZEITSCHRIFT, 2023, 303 (02)

← 1 2 3 4 5 →