Elementary spectral invariants and quantitative closing lemmas for contact three-manifolds
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866907865574277120 |
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| author | Hutchings, Michael |
| author_facet | Hutchings, Michael |
| contents | In a previous paper, we defined an "elementary" alternative to the ECH capacities of symplectic four-manifolds, using max-min energy of holomorphic curves subject to point constraints, and avoiding the use of Seiberg-Witten theory. In the present paper we use a variant of this construction to define an alternative to the ECH spectrum of a contact three-manifold. The alternative spectrum has applications to Reeb dynamics in three dimensions. In particular, we adapt ideas from a previous joint paper with Edtmair to obtain quantitative closing lemmas for Reeb vector fields in three dimensions. For the example of an irrational ellipsoid, we obtain a sharp quantitative closing lemma. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_01767 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Elementary spectral invariants and quantitative closing lemmas for contact three-manifolds Hutchings, Michael Symplectic Geometry Dynamical Systems In a previous paper, we defined an "elementary" alternative to the ECH capacities of symplectic four-manifolds, using max-min energy of holomorphic curves subject to point constraints, and avoiding the use of Seiberg-Witten theory. In the present paper we use a variant of this construction to define an alternative to the ECH spectrum of a contact three-manifold. The alternative spectrum has applications to Reeb dynamics in three dimensions. In particular, we adapt ideas from a previous joint paper with Edtmair to obtain quantitative closing lemmas for Reeb vector fields in three dimensions. For the example of an irrational ellipsoid, we obtain a sharp quantitative closing lemma. |
| title | Elementary spectral invariants and quantitative closing lemmas for contact three-manifolds |
| topic | Symplectic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2208.01767 |