We introduce a new method of constructing Birkhoff sections for pseudo-Anosov flows, which uses the connection between pseudo-Anosov flows and veering triangulations. This method allows for explicit constructions, as well as control over the Birkhoff section in terms of its Euler characteristic and the complexity of the boundary orbits. In particular, we show that any transitive pseudo-Anosov flow has a Birkhoff section with two boundary components.

中文翻译：

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以受控复杂度构建伪阿诺索夫流的 Birkhoff 截面

我们引入了一种为伪阿诺索夫流构造 Birkhoff 截面的新方法，该方法利用伪阿诺索夫流和转向三角剖分之间的联系。该方法允许显式构造，以及根据其欧拉特性和边界轨道的复杂性来控制伯霍夫截面。特别是，我们证明任何传递伪阿诺索夫流都具有带有两个边界分量的伯克霍夫截面。