Depth-one foliations, pseudo-Anosov flows and universal circles
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910643754369024 |
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| author | Huang, Junzhi |
| author_facet | Huang, Junzhi |
| contents | Given a taut depth-one foliation $\mathcal{F}$ in a closed atoroidal 3-manifold $M$ transverse to a pseudo-Anosov flow $ϕ$ without perfect fits, we show that the universal circle coming from leftmost sections $\mathfrak{S}_\mathrm{left}$ associated to $\mathcal{F}$, constructed by Thurston and Calegari-Dunfield, is isomorphic to the ideal boundary of the flow space associated to $ϕ$ with natural structure maps. As a corollary, we use a theorem of Barthelmé-Frankel-Mann to show that there is at most one pseudo-Anosov flow without perfect fits transverse to $\mathcal{F}$ up to orbit equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07559 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Depth-one foliations, pseudo-Anosov flows and universal circles Huang, Junzhi Geometric Topology Given a taut depth-one foliation $\mathcal{F}$ in a closed atoroidal 3-manifold $M$ transverse to a pseudo-Anosov flow $ϕ$ without perfect fits, we show that the universal circle coming from leftmost sections $\mathfrak{S}_\mathrm{left}$ associated to $\mathcal{F}$, constructed by Thurston and Calegari-Dunfield, is isomorphic to the ideal boundary of the flow space associated to $ϕ$ with natural structure maps. As a corollary, we use a theorem of Barthelmé-Frankel-Mann to show that there is at most one pseudo-Anosov flow without perfect fits transverse to $\mathcal{F}$ up to orbit equivalence. |
| title | Depth-one foliations, pseudo-Anosov flows and universal circles |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2410.07559 |