三维Reeb流C∞闭引理的注释

IF 0.5 4区数学 Q3 MATHEMATICS

Kyoto Journal of Mathematics Pub Date : 2021-01-01 DOI:10.1215/21562261-2021-0003

Kei Irie

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引用次数: 1

摘要

我们证明了三维Reeb流的c∞闭引理的两个改进，并作为嵌入式接触同调(ECH)的谱不变量的应用证明了这两个改进。具体地说，我们证明了以下两个结果:(i)对于任意闭3流形上的aC∞-一般接触形式，表示ECH同调类的周期Reeb轨道的并是密集的;(ii)三维Reeb流的C∞闭引理的实解析形式。本文还讨论了与这些结果有关的一些问题和猜想。

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Remarks about the C∞-closing lemma for 3-dimensional Reeb flows

We prove two refinements of theC∞-closing lemma for 3-dimensional Reeb flows, which was proved by the author as an application of spectral invariants ofEmbedded Contact Homology (ECH). Specifically, we prove the following two results: (i) for aC∞-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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来源期刊

Kyoto Journal of Mathematics MATHEMATICS-

CiteScore

1.10

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： The Kyoto Journal of Mathematics publishes original research papers at the forefront of pure mathematics, including surveys that contribute to advances in pure mathematics.