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arXiv · 1812.06058

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

Kyrylo Muliarchyk·Serhii Dovhyi
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Abstract

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 $LO(F_2)$ has no isolated points, where $F_2$ is a free group on two generators. In this paper we show that $O(F_2)$ has no isolated points as well.

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Kyrylo Muliarchyk, Serhii Dovhyi. 2018-12-14. Topology of the space of bi-orderings of a free group on two generators. https://arxiv.org/abs/1812.06058

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