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arXiv · 2410.07559

Depth-one foliations, pseudo-Anosov flows and universal circles

Junzhi Huang
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Abstract

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.

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Junzhi Huang. 2024-10-10. Depth-one foliations, pseudo-Anosov flows and universal circles. https://arxiv.org/abs/2410.07559

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