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].
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页码：613 / 632
页数：20
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