Selective Floer cohomology for contact vector fields
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917661894508544 |
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| author | Cant, Dylan Uljarević, Igor |
| author_facet | Cant, Dylan Uljarević, Igor |
| contents | This paper associates a persistence module to a contact vector field $X$ on the ideal boundary of a Liouville manifold. The persistence module measures the dynamics of $X$ on the region $Ω$ where $X$ is positively transverse to the contact distribution. The colimit of the persistence module depends only on the domain $Ω$ and is a variant of the selective symplectic homology introduced by the second named author. As an application we prove existence of positive orbits for certain classes of contact vector fields. Another application of this invariant is that we recover the famous non-squeezing result of Eliashberg, Kim, and Polterovich. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05443 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Selective Floer cohomology for contact vector fields Cant, Dylan Uljarević, Igor Symplectic Geometry 53D40, 53D10 This paper associates a persistence module to a contact vector field $X$ on the ideal boundary of a Liouville manifold. The persistence module measures the dynamics of $X$ on the region $Ω$ where $X$ is positively transverse to the contact distribution. The colimit of the persistence module depends only on the domain $Ω$ and is a variant of the selective symplectic homology introduced by the second named author. As an application we prove existence of positive orbits for certain classes of contact vector fields. Another application of this invariant is that we recover the famous non-squeezing result of Eliashberg, Kim, and Polterovich. |
| title | Selective Floer cohomology for contact vector fields |
| topic | Symplectic Geometry 53D40, 53D10 |
| url | https://arxiv.org/abs/2405.05443 |