Diagram groups, braid groups, and orderability

被引：4

作者：

Wiest, B ^{[1
]}

机构：

[1] Univ Rennes 1, UFR Math, F-35042 Rennes, France

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2003年 / 12卷 / 03期

关键词：

diagram group; braid group; Thompson group; orderable group;

D O I：

10.1142/S0218216503002482

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that all diagram groups (in the sense of Guba and Sapir) are left-orderable. The proof is in two steps: firstly, it is proved that all diagram groups inject in a certain braid group on infinitely many strings, and secondly, this group is then shown to be left-orderable.

引用

页码：321 / 332

页数：12

共 50 条

[21] Ordering the braid groups
Fenn, R
Greene, MT
Rolfsen, D
Rourke, C
Wiest, B
PACIFIC JOURNAL OF MATHEMATICS, 1999, 191 (01) : 49 - 74
[22] Braid groups are linear
Krammer, D
ANNALS OF MATHEMATICS, 2002, 155 (01) : 131 - 156
[23] On marked braid groups
Fedoseev, Denis A.
Manturov, Vassily O.
Cheng, Zhiyun
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2015, 24 (13)
[24] On quotients of braid groups
Leung, KH
Wong, YL
COMMUNICATIONS IN ALGEBRA, 1996, 24 (08) : 2535 - 2549
[25] Orders on Braid Groups
N. Ya. Medvedev
Algebra and Logic, 2003, 42 (3) : 177 - 180
[26] Braid groups are linear
Bigelow, SJ
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 14 (02) : 471 - 486
[27] HILDEN BRAID GROUPS
Bellingeri, P.
Cattabriga, A.
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2012, 21 (03)
[28] GENERALIZED BRAID GROUPS
DELIGNE, P
INVENTIONES MATHEMATICAE, 1972, 17 (04) : 273 - &
[29] On braid groups in handlebodies
Vershinin, VV
SIBERIAN MATHEMATICAL JOURNAL, 1998, 39 (04) : 645 - 654
[30] On braid groups in handlebodies
V. V. Vershinin
Siberian Mathematical Journal, 1998, 39 : 645 - 654

← 1 2 3 4 5 →