AI 中文总结
研究环面三维流形上伪阿诺索夫轨道空间通用圆的层叠$\Lambda^\pm_u$，证明其由轨道空间边界的稳定和不稳定预层叠确定，且对特定作用，存在有限层叠对集合，使相关最小轨道空间通用圆的$(\Lambda^+_u,\Lambda^-_u)$在其中。
AI 中文摘要
卡莱加里引入了与通用圆相关的层叠$\Lambda^\pm_u$。我们研究了环面三维流形上紧叶状结构的伪阿诺索夫轨道空间通用圆的层叠$\Lambda^\pm_u$。我们证明$\Lambda^+_u$和$\Lambda^-_u$完全由轨道空间边界上的稳定和不稳定预层叠确定。然后，利用巴特尔梅、博纳蒂和曼的结果，我们证明对于任何来自伪阿诺索夫流轨道空间的作用$\rho:\pi_1(M)\to \mathrm{Homeo}^+(S^1)$，存在有限的层叠对集合，使得对于任何作用与$\rho$共轭的最小轨道空间通用圆，$(\Lambda^+_u,\Lambda^-_u)$都在该集合中。
英文摘要
Calegari introduced the laminations $Λ^\pm_u$ associated to a universal circle. We study the laminations $Λ^\pm_u$ for pseudo-Anosov orbit space universal circles of taut foliations, on atoroidal three-manifolds. We prove that $Λ^+_u$ and $Λ^-_u$ are completely determined by the stable and unstable prelaminations on the boundary of the orbit space. Then, using a result of Barthelmé, Bonatti, and Mann, we prove that for any action $ρ:π_1(M)\to \mathrm{Homeo}^+(S^1)$ coming from an orbit space of a pseudo-Anosov flow, there is a finite collection of lamination pairs such that $(Λ^+_u,Λ^-_u)$ lies in this collection for any minimal orbit space universal circle whose action is conjugate to $ρ$.
