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arXiv · 1902.01172

A Reeb flow on the three-sphere without a disk-like global surface of section

Otto van Koert
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Abstract

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.

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Otto van Koert. 2019-02-04. A Reeb flow on the three-sphere without a disk-like global surface of section. https://arxiv.org/abs/1902.01172

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