On the Borel complexity of the space of left-orderings of nilpotent groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912473116835840 |
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| author | Taucán, Emir Molina |
| author_facet | Taucán, Emir Molina |
| contents | We give the first examples of nonabelian left-orderable groups such that the conjugacy orbit equivalence relation on its space of orders has infinity orbits, yet it is smooth in the Borel sense. The examples are all nilpotent groups and we provide a sufficient condition so that the space of orders of a nilpotent group has a smooth conjugacy orbit relation. We also show with different examples that nilpotence is not a sufficient condition for smoothness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06953 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Borel complexity of the space of left-orderings of nilpotent groups Taucán, Emir Molina Group Theory Dynamical Systems Logic 03E15, 06F15, 20F18, 20F60 We give the first examples of nonabelian left-orderable groups such that the conjugacy orbit equivalence relation on its space of orders has infinity orbits, yet it is smooth in the Borel sense. The examples are all nilpotent groups and we provide a sufficient condition so that the space of orders of a nilpotent group has a smooth conjugacy orbit relation. We also show with different examples that nilpotence is not a sufficient condition for smoothness. |
| title | On the Borel complexity of the space of left-orderings of nilpotent groups |
| topic | Group Theory Dynamical Systems Logic 03E15, 06F15, 20F18, 20F60 |
| url | https://arxiv.org/abs/2507.06953 |