We prove a bi-ordered version of Rivas' result for free products of left-order groups. Namely, we show that a free product of bi-ordered groups does not admit isolated bi-ordering. Our method relies on the dynamical realization of bi-ordered groups. We also show that the natural action of the automorphism group Aut(F₂) on F₂ does not have dense orbits.
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Kyrylo Muliarchyk (2024) studied this question.
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