We show that there are Reeb flows on the standard, tight three-sphere that do not admit global surfaces of section with one boundary component. In particular, the Reeb flows that we construct do not admit disk-like global surfaces of section. These Reeb flows are constructed using integrable systems, and a connected sum construction that extends the integrable system.

中文翻译：

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没有球面像整体截面的三球面上的Reeb流

我们表明，在标准的紧密三球体上存在Reeb流动，这些流动不容许具有一个边界分量的截面的整体表面。特别是，我们构造的Reeb流不允许截面为圆盘状的整体表面。这些Reeb流使用可积系统和扩展可积系统的连接和构造构成。