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] Blocked-Braid Groups
D. Maglia
N. Sabadini
R. F. C. Walters
Applied Categorical Structures, 2015, 23 : 53 - 61
[22] Remark on ordered braid groups
Nikolaev, Igor V.
JOURNAL OF TOPOLOGY AND ANALYSIS, 2023, : 1 - 13
[23] Characteristics of Graph Braid Groups
Ko, Ki Hyoung
Park, Hyo Won
DISCRETE & COMPUTATIONAL GEOMETRY, 2012, 48 (04) : 915 - 963
[24] Local representations of braid groups
Mikhalchishina, Yu A.
SIBERIAN MATHEMATICAL JOURNAL, 2013, 54 (04) : 666 - 678
[25] On word reversing in braid groups
Dehornoy, Patrick
Wiest, Bert
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2006, 16 (05) : 941 - 957
[26] Local representations of braid groups
Yu. A. Mikhalchishina
Siberian Mathematical Journal, 2013, 54 : 666 - 678
[27] Braid pictures for Artin groups
Allcock, D
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 354 (09) : 3455 - 3474
[28] Automorphisms of pure braid groups
Valeriy G. Bardakov
Mikhail V. Neshchadim
Mahender Singh
Monatshefte für Mathematik, 2018, 187 : 1 - 19
[29] GEOMETRIC REPRESENTATIONS OF THE BRAID GROUPS
Castel, Fabrice
ASTERISQUE, 2016, (378) : 1 - +
[30] UNIVERSAL REPRESENTATIONS OF BRAID AND BRAID-PERMUTATION GROUPS
Berceanu, Barbu
Papadima, Stefan
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2009, 18 (07) : 999 - 1019

← 1 2 3 4 5 →