On the topology of the space of bi-orderings of a free group on two generators

被引：1

作者：

Dovhyi, Serhii ^{[1
]}

Muliarchyk, Kyrylo ^{[2
]}

机构：

[1] Univ Manitoba, Fac Grad Studies, 1454 William St, Vancouver, BC V5L 2P9, Canada

[2] Univ Texas Austin, Dept Math, 2515 Speedway,PMA 8-100, Austin, TX 78712 USA

来源：

GROUPS GEOMETRY AND DYNAMICS | 2023年 / 17卷 / 02期

关键词：

Sikora conjecture; bi-ordered groups;

D O I：

10.4171/GGD/712

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a group. We can topologize the spaces of left-orderings LO(G) and bi-orderings O(G) of G with the product topology. These spaces may or may not have isolated points. It is known that LO(Fn) has no isolated points, where Fn is a free group on n > 2 generators. In this paper, we show that O(Fn) has no isolated points as well, thereby resolving the second part of Conjecture 2.2 by Sikora [Bull. London Math. Soc. 36 (2004), 519-526].

引用

页码：613 / 632

页数：20

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