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

[摘要] Let GGG be a group. We can topologize the spaces of left-orderings LO⁡(G)\operatorname{LO}(G)LO(G) and bi-orderings O⁡(G)\operatorname{O}(G)O(G) of GGG with the product topology. These spaces may or may not have isolated points. It is known that LO⁡(Fn)\operatorname{LO}(F_n)LO(Fn​) has no isolated points, where FnF_nFn​ is a free group on n≥2n\geq 2n≥2 generators. In this paper, we show that O⁡(Fn)\operatorname{O}(F_n)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].

[学科分类] 神经科学

[关键词] Sikora conjecture;bi-ordered groups