Left orderability and taut foliations with orderable cataclysm
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917306323435520 |
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| author | Zhao, Bojun |
| author_facet | Zhao, Bojun |
| contents | Let $M$ be a connected, closed, orientable, irreducible $3$-manifold. We show that: if $M$ admits a co-orientable taut foliation $\mathcal{F}$ with orderable cataclysm, then $π_1(M)$ is left orderable. This provides an elementary proof that $π_1(M)$ is left orderable if $M$ admits an Anosov flow with a co-orientable stable foliation without using Thurston's universal circle action. Furthermore, for every closed orientable 3-manifold that admits a pseudo-Anosov flow $X$ with a co-orientable stable foliation, our result applies to infinitely many of Dehn fillings along the union of singular orbits of $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_04719 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Left orderability and taut foliations with orderable cataclysm Zhao, Bojun Geometric Topology Let $M$ be a connected, closed, orientable, irreducible $3$-manifold. We show that: if $M$ admits a co-orientable taut foliation $\mathcal{F}$ with orderable cataclysm, then $π_1(M)$ is left orderable. This provides an elementary proof that $π_1(M)$ is left orderable if $M$ admits an Anosov flow with a co-orientable stable foliation without using Thurston's universal circle action. Furthermore, for every closed orientable 3-manifold that admits a pseudo-Anosov flow $X$ with a co-orientable stable foliation, our result applies to infinitely many of Dehn fillings along the union of singular orbits of $X$. |
| title | Left orderability and taut foliations with orderable cataclysm |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2210.04719 |