A vanishing property about the 1-filtered cohomology groups of (4n+2)-dimensional closed symplectic manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912644159504384 |
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| author | Zhuang, Hao |
| author_facet | Zhuang, Hao |
| contents | This note is a follow-up to our previous work arXiv:2505.14496. For any (4n+2)-dimensional closed symplectic manifold, we find that the dimension of the even-degree part of its 1-filtered cohomology is even, similar to the vanishing property of the classical Euler characteristic of an odd-dimensional closed manifold. We prove our result by constructing and then deforming a skew-adjoint operator. This process follows the methods in arXiv:2505.14496 but needs adjustments on signs and the power of the symplectic form. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_10630 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A vanishing property about the 1-filtered cohomology groups of (4n+2)-dimensional closed symplectic manifolds Zhuang, Hao Symplectic Geometry Differential Geometry 58J20 (Primary), 53D05 (Secondary) This note is a follow-up to our previous work arXiv:2505.14496. For any (4n+2)-dimensional closed symplectic manifold, we find that the dimension of the even-degree part of its 1-filtered cohomology is even, similar to the vanishing property of the classical Euler characteristic of an odd-dimensional closed manifold. We prove our result by constructing and then deforming a skew-adjoint operator. This process follows the methods in arXiv:2505.14496 but needs adjustments on signs and the power of the symplectic form. |
| title | A vanishing property about the 1-filtered cohomology groups of (4n+2)-dimensional closed symplectic manifolds |
| topic | Symplectic Geometry Differential Geometry 58J20 (Primary), 53D05 (Secondary) |
| url | https://arxiv.org/abs/2510.10630 |