Topology of Anosov flows and Birkhoff sections

3 流形上的传递阿诺索夫流可以描述为通过 Dehn 手术从表面伪阿诺索夫图的悬浮流获得的流。此类 3 流形表面的图像称为 Birkhoff 截面。我们尝试使用 Birkhodd 截面来理解 3 流形上的阿诺索夫流的拓扑结构。在 Kamatani、Kodama 和 Noda 的工作中，已经为 Anosov 流的 Bonatti-Langevin 例子找到了属 0 的 Birkhoff 部分。在这项工作中，我们研究了同一流中属 1 的 Birkhoff 截面的存在性。

Transitive Anosov flows on 3-manifolds can be described as ones obtained by Dehn surgeries from suspension flows of pseudo-Anosov maps of surfaces. The images of such surfaces in 3-manifolds are called Birkhoff sections. We try to understand the topology of Anosov flows on 3-manifolds using Birkhodd sections. In the work of Kamatani, Kodama and Noda, a Birkhoff section of genus 0 has been found for the Bonatti-Langevin example of Anosov flow. In this work, we study the existence of Birkhoff sections of genus 1 for the same flow.