Topology of Anosov flows and Birkhoff sections

三维流形上的传递Anosov流可以描述为由曲面的伪Anosov映射的悬浮流通过Dehn手术得到的流。这种曲面在三维流形中的像称为Birkhoff截面。我们试图了解拓扑的Anosov流的三维流形上使用Birkhodd部分。在Kamatani，Kodama和Noda的工作中，对于Anosov流的Bonatti-Langevin例子，发现了亏格为0的Birkhoff截面。在这项工作中，我们研究了存在的Birkhoff截面亏格1相同的流。

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.