$S^1$-equivariant relative symplectic cohomology and relative symplectic capacities
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913531639627776 |
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| author | Ahn, Jonghyeon |
| author_facet | Ahn, Jonghyeon |
| contents | In this paper, we construct an $S^1$-equivariant version of the relative symplectic cohomology developed by Varolgunes. As an application, we construct a relative version of Gutt-Hutchings capacities and a relative version of symplectic (co)homology capacity. We will see that these relative symplectic capacities can detect the diplaceability and the heaviness of a compact subset of a symplectic manifold. We compare the first relative Gutt-Hutchings capacity and the relative symplectic (co)homology capacity and prove that they are equal to each other under a convexity assumption. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01977 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $S^1$-equivariant relative symplectic cohomology and relative symplectic capacities Ahn, Jonghyeon Symplectic Geometry In this paper, we construct an $S^1$-equivariant version of the relative symplectic cohomology developed by Varolgunes. As an application, we construct a relative version of Gutt-Hutchings capacities and a relative version of symplectic (co)homology capacity. We will see that these relative symplectic capacities can detect the diplaceability and the heaviness of a compact subset of a symplectic manifold. We compare the first relative Gutt-Hutchings capacity and the relative symplectic (co)homology capacity and prove that they are equal to each other under a convexity assumption. |
| title | $S^1$-equivariant relative symplectic cohomology and relative symplectic capacities |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2410.01977 |