Strong closing property of contact forms and action selecting functors
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913258942758912 |
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| author | Irie, Kei |
| author_facet | Irie, Kei |
| contents | We introduce a notion of strong closing property of contact forms, inspired by the $C^\infty$ closing lemma for Reeb flows in dimension three. We then prove a sufficient criterion for strong closing property, which is formulated by considering a monoidal functor from a category of manifolds with contact forms to a category of filtered vector spaces. As a potential application of this criterion, we propose a conjecture which says that a standard contact form on the boundary of any symplectic ellipsoid satisfies strong closing property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_09216 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Strong closing property of contact forms and action selecting functors Irie, Kei Symplectic Geometry Dynamical Systems 70H12, 53D42 We introduce a notion of strong closing property of contact forms, inspired by the $C^\infty$ closing lemma for Reeb flows in dimension three. We then prove a sufficient criterion for strong closing property, which is formulated by considering a monoidal functor from a category of manifolds with contact forms to a category of filtered vector spaces. As a potential application of this criterion, we propose a conjecture which says that a standard contact form on the boundary of any symplectic ellipsoid satisfies strong closing property. |
| title | Strong closing property of contact forms and action selecting functors |
| topic | Symplectic Geometry Dynamical Systems 70H12, 53D42 |
| url | https://arxiv.org/abs/2201.09216 |