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

2018/12/14 by Muliarchyk, Kyrylo, Dovhyi, Serhii
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1812.06058

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(F₂) has no isolated points, where F₂ is a free group on two generators. In this paper we show that O(F₂) has no isolated points as well.

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