Geodesic
On the topology of the space of bi-orderings of a free group on two generators
Serhii Dovhyi1 ; Kyrylo Muliarchyk2
1University of Manitoba, Vancouver, Canada
2University of Texas at Austin, USA
Groups, geometry, and dynamics, Tome 17 (2023) no. 2, pp. 613-632

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DOI

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].
DOI : 10.4171/ggd/712
Classification : 20-XX, 06-XX
Mots-clés : Sikora conjecture, bi-ordered groups

Serhii Dovhyi  1   ; Kyrylo Muliarchyk  2

1 University of Manitoba, Vancouver, Canada
2 University of Texas at Austin, USA 
Serhii Dovhyi; Kyrylo Muliarchyk. On the topology of the space of bi-orderings of a free group on two generators. Groups, geometry, and dynamics, Tome 17 (2023) no. 2, pp. 613-632. doi: 10.4171/ggd/712
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