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
收藏
页码：540 / 547
页数：8
相关论文
共 50 条
  • [1] Homology computations for complex braid groups
    Callegaro, Filippo
    Marin, Ivan
    JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2014, 16 (01) : 103 - 164
  • [2] Homology of tree braid groups
    Farley, D
    Topological and Asymptotic Aspects of Group Theory, 2006, 394 : 101 - 112
  • [3] Asymptotic homology of graph braid groups
    An, Byung Hee
    Drummond-cole, Gabriel C.
    Knudsen, B. E. N.
    GEOMETRY & TOPOLOGY, 2022, 26 (04) : 1745 - 1771
  • [4] On the second homology of planar graph braid groups
    An, Byung Hee
    Knudsen, Ben
    JOURNAL OF TOPOLOGY, 2022, 15 (02) : 666 - 691
  • [5] Edge stabilization in the homology of graph braid groups
    An, Byung Hee
    Drummond-Cole, Gabriel C.
    Knudsen, Ben
    GEOMETRY & TOPOLOGY, 2020, 24 (01) : 421 - 469
  • [6] The homology of the Milnor fiber for classical braid groups
    Callegaro, Filippo
    ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2006, 6 : 1903 - 1923
  • [7] Stability phenomena in the homology of tree braid groups
    Ramos, Eric
    ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2018, 18 (04): : 2305 - 2337
  • [8] Braid groups, mapping class groups and their homology with twisted coefficients
    Bianchi, Andrea
    MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2022, 172 (02) : 249 - 266
  • [9] Braid groups in complex spaces
    Manfredini, Sandro
    Parveen, Saima
    Settepanella, Simona
    BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 2014, 7 (02): : 157 - 168
  • [10] Braid groups in complex Grassmannians
    Manfredini, Sandro
    Settepanella, Simona
    TOPOLOGY AND ITS APPLICATIONS, 2014, 176 : 51 - 56
12345