Algorithmic aspects of left-orderings of solvable Baumslag--Solitar groups via its dynamical realization

2024/05/14 by Ho, Meng-Che "Turbo", Le, Khanh, Rossegger, Dino
#03C57 #03D45 #03E15 #20F60 #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · doi:10.48550/arxiv.2405.08442

Abstract

We answer a question of Calderoni and Clay by showing that the conjugation equivalence relation of left orderings of the Baumslag-Solitar groups BS(1,n) is hyperfinite for any n. Our proof relies on a classification of BS(1,n)'s left-orderings via its one-dimensional dynamical realizations. We furthermore use the effectiveness of the dynamical realizations of BS(1,n) to study algorithmic properties of the left-orderings on BS(1,n).

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