Topology of Anosov flows and Birkhoff sections

三维流形上的传递Anosov流可以描述为Dehn手术从曲面的伪Anosov映射的悬浮流中得到的Anosov流。这种曲面在三维流形上的像称为Birkhoff截面。我们试图利用Birkhodd截面来理解三维流形上的Anosov流的拓扑。在Kamatani、KoDama和Noda的工作中，对于Anosov流的Bonatti-Langevin例子，已经发现了亏格为0的Birkhoff截面。在这项工作中，我们研究了同一流的亏格为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.