带应用于伪阿诺索夫流的转向三角剖分钻孔
Drilling veering triangulations with applications to pseudo-Anosov flows
- Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克科学促进研究所数学系）
- Oklahoma State University（俄克拉荷马州立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文开发了一种转向三角剖分钻孔算法，用于构造转向母三角剖分，应用于伪阿诺索夫流的闭轨道钻孔，为Ghys关于传递阿诺索夫流的猜想提供了计算证据。
AI中文摘要：
我们开发了一种算法，其输入为转向三角剖分V和V的一个流环c，输出为V的转向母三角剖分V_c。构造转向母三角剖分将传递伪阿诺索夫流的闭轨道钻孔操作组合化。该算法依赖于充分细致地局部近似与V相关的织机空间结构，以实现Agol-Guéritaud构造的特定修改。我们利用该钻孔算法的实现，构造非层状转向三角剖分的层状母三角剖分（进而得到传递伪阿诺索夫流的Birkhoff截面），以及非几何转向三角剖分的几何母三角剖分。我们还发现（钻孔后）伪阿诺索夫流的闭轨道，它们在环境中不与其自由同伦类中的测地线同痕，并证明某些转向三角剖分编码几乎轨道等价的流。特别地，我们为Ghys的一个猜想提供了新的计算证据，该猜想断言所有具有可定向不变叶状结构的传递阿诺索夫流都是几乎轨道等价的。
英文摘要：
We develop an algorithm that takes as input a veering triangulation V and a flow cycle c of V, and outputs a veering parent V_c of V. Constructing veering parents combinatorializes drilling out closed orbits of transitive pseudo-Anosov flows. The algorithm relies on locally approximating the structure of the loom space associated to V in sufficient detail to carry out a certain modification of the Agol-Guéritaud construction. We use an implementation of the drilling algorithm to construct layered parents of non-layered veering triangulations (and hence Birkhoff sections for transitive pseudo-Anosov flows) and geometric parents of non-geometric veering triangulations. We also find closed orbits of (drilled) pseudo-Anosov flows that are not ambiently isotopic to the geodesics in their free homotopy classes, and show that certain veering triangulations encode almost orbit equivalent flows. In particular, we provide new computational evidence for a conjecture of Ghys asserting that all transitive Anosov flows with orientable invariant foliations are almost orbit equivalent.
