Left-orderability of Groups Acting on Bifoliated Planes
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914790207651840 |
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| author | Camargo-Rios, Mauro Lu, Lingfeng |
| author_facet | Camargo-Rios, Mauro Lu, Lingfeng |
| contents | We prove that any group acting faithfully on a bifoliated plane while preserving the orientations of both foliations is left-orderable. The proof utilizes a construction of a linear order on the set of ends of the leaf spaces, which takes advantage of the additional structure coming with a bifoliation. Moreover, we build an identification between ends of leaf spaces of the bifoliation and subsets of the boundary circle at infinity, and use it to give a condition for the equivalence between a faithful group action on a bifoliated plane and a faithful group action on the set of ends of the leaf spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06169 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Left-orderability of Groups Acting on Bifoliated Planes Camargo-Rios, Mauro Lu, Lingfeng Geometric Topology Group Theory We prove that any group acting faithfully on a bifoliated plane while preserving the orientations of both foliations is left-orderable. The proof utilizes a construction of a linear order on the set of ends of the leaf spaces, which takes advantage of the additional structure coming with a bifoliation. Moreover, we build an identification between ends of leaf spaces of the bifoliation and subsets of the boundary circle at infinity, and use it to give a condition for the equivalence between a faithful group action on a bifoliated plane and a faithful group action on the set of ends of the leaf spaces. |
| title | Left-orderability of Groups Acting on Bifoliated Planes |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2405.06169 |