A characterization of heaviness in terms of relative symplectic cohomology
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916157927194624 |
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| author | Mak, Cheuk Yu Sun, Yuhan Varolgunes, Umut |
| author_facet | Mak, Cheuk Yu Sun, Yuhan Varolgunes, Umut |
| contents | For a compact subset $K$ of a closed symplectic manifold $(M, ω)$, we prove that $K$ is heavy if and only if its relative symplectic cohomology over the Novikov field is non-zero. As an application we show that if two compact sets are not heavy and Poisson commuting, then their union is also not heavy. A discussion on superheaviness together with some partial results are also included. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_12625 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A characterization of heaviness in terms of relative symplectic cohomology Mak, Cheuk Yu Sun, Yuhan Varolgunes, Umut Symplectic Geometry 53D40 For a compact subset $K$ of a closed symplectic manifold $(M, ω)$, we prove that $K$ is heavy if and only if its relative symplectic cohomology over the Novikov field is non-zero. As an application we show that if two compact sets are not heavy and Poisson commuting, then their union is also not heavy. A discussion on superheaviness together with some partial results are also included. |
| title | A characterization of heaviness in terms of relative symplectic cohomology |
| topic | Symplectic Geometry 53D40 |
| url | https://arxiv.org/abs/2301.12625 |