Algorithmic aspects of left-orderings of solvable Baumslag--Solitar groups via its dynamical realization
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916245851340800 |
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| author | Ho, Meng-Che "Turbo" Le, Khanh Rossegger, Dino |
| author_facet | Ho, Meng-Che "Turbo" Le, Khanh Rossegger, Dino |
| contents | We answer a question of Calderoni and Clay by showing that the conjugation equivalence relation of left orderings of the Baumslag-Solitar groups $\mathrm{BS}(1,n)$ is hyperfinite for any $n$. Our proof relies on a classification of $\mathrm{BS}(1,n)$'s left-orderings via its one-dimensional dynamical realizations. We furthermore use the effectiveness of the dynamical realizations of $\mathrm{BS}(1,n)$ to study algorithmic properties of the left-orderings on $\mathrm{BS}(1,n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08442 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algorithmic aspects of left-orderings of solvable Baumslag--Solitar groups via its dynamical realization Ho, Meng-Che "Turbo" Le, Khanh Rossegger, Dino Logic Group Theory 03E15, 20F60, 03C57, 03D45 We answer a question of Calderoni and Clay by showing that the conjugation equivalence relation of left orderings of the Baumslag-Solitar groups $\mathrm{BS}(1,n)$ is hyperfinite for any $n$. Our proof relies on a classification of $\mathrm{BS}(1,n)$'s left-orderings via its one-dimensional dynamical realizations. We furthermore use the effectiveness of the dynamical realizations of $\mathrm{BS}(1,n)$ to study algorithmic properties of the left-orderings on $\mathrm{BS}(1,n)$. |
| title | Algorithmic aspects of left-orderings of solvable Baumslag--Solitar groups via its dynamical realization |
| topic | Logic Group Theory 03E15, 20F60, 03C57, 03D45 |
| url | https://arxiv.org/abs/2405.08442 |