The K(rr, 1)-conjecture implies the center conjecture for Artin groups

被引：3

作者：

Jankiewicz, Kasia ^{[1
]}

Schreve, Kevin ^{[2
]}

机构：

[1] Univ Calif Santa Cruz, Dept Math, Santa Cruz, CA 95064 USA

[2] Louisiana State Univ, Dept Math, Baton Rouge, LA 70806 USA

来源：

JOURNAL OF ALGEBRA | 2023年 / 615卷

关键词：

Artin groups; Center; TheK(?1)-conjecture; TITS;

D O I：

10.1016/j.jalgebra.2022.10.024

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note, we prove that the K(pi,1)-conjecture for Artin groups implies the center conjecture for Artin groups. Specifically, every Artin group without a spherical factor that satisfies the K(pi,1)-conjecture has a trivial center.(c) 2022 Elsevier Inc. All rights reserved.

引用

页码：455 / 463

页数：9

共 20 条

[1] [Anonymous], 2014, ANN FAC SCI TOULOUSE
[2] Non-positively curved aspects of Artin groups of finite type
Bestvina, Mladen
[J]. GEOMETRY & TOPOLOGY, 1999, 3 : 269 - 302
[3] Bieri R, 1981, HOMOLOGICAL DIMENSIO
[4] ARTIN GROUPS AND COXETER GROUPS
BRIESKORN, E
SAITO, K
[J]. INVENTIONES MATHEMATICAE, 1972, 17 (04) : 245 - +
[5] The Deligne complex for the four-strand braid group
Charney, R
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 356 (10) : 3881 - 3897
[6] THE K(PI,1)-PROBLEM FOR HYPERPLANE COMPLEMENTS ASSOCIATED TO INFINITE REFLECTION GROUPS
CHARNEY, R
DAVIS, MW
[J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 8 (03) : 597 - 627
[7] The Tits conjecture for locally reducible Artin groups
Charney, R
[J]. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2000, 10 (06) : 783 - 797
[8] ARTIN GROUPS OF INFINITE TYPE: TRIVIAL CENTERS AND ACYLINDRICAL HYPERBOLICITY
Charney, Ruth
Morris-Wright, Rose
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 147 (09) : 3675 - 3689
[9] Crisp J, 1999, GEOMETRIC GROUP THEORY DOWN UNDER, P119
[10] The solution to a conjecture of Tits on the subgroup generated by the squares of the generators of an Artin group
Crisp, J
Paris, L
[J]. INVENTIONES MATHEMATICAE, 2001, 145 (01) : 19 - 36

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