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June 2021 Remarks about the C-closing lemma for 3-dimensional Reeb flows
Kei Irie
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Kyoto J. Math. 61(2): 305-322 (June 2021). DOI: 10.1215/21562261-2021-0003

Abstract

We prove two refinements of the C-closing lemma for 3-dimensional Reeb flows, which was proved by the author as an application of spectral invariants of Embedded Contact Homology (ECH). Specifically, we prove the following two results: (i) for a C-generic contact form on any closed 3-manifold, the union of periodic Reeb orbits representing ECH homology classes is dense; (ii) a certain real-analytic version of the C-closing lemma for 3-dimensional Reeb flows. A few questions and conjectures related to these results are also discussed.

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Kei Irie. "Remarks about the C-closing lemma for 3-dimensional Reeb flows." Kyoto J. Math. 61 (2) 305 - 322, June 2021. https://doi.org/10.1215/21562261-2021-0003

Information

Received: 9 January 2020; Revised: 1 August 2020; Accepted: 17 August 2020; Published: June 2021
First available in Project Euclid: 22 March 2021

Digital Object Identifier: 10.1215/21562261-2021-0003

Subjects:
Primary: 70H12

Rights: Copyright © 2021 by Kyoto University

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Vol.61 • No. 2 • June 2021
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