Cohomologous symplectic forms with different Gromov widths
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909610567270400 |
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| author | Ning, Shengzhen |
| author_facet | Ning, Shengzhen |
| contents | We study McDuff-Salamon's Problem 46 by showing that there exist closed manifolds of dimension $\geq 6$ admitting cohomologous symplectic forms with different Gromov widths. The examples are motivated by Ruan's early example of deformation inequivalent symplectic forms in dimension $6$ distinguished by Gromov-Witten invariants. To find cohomologous symplectic forms and compare their Gromov width, we make use of Li-Liu's theorem of symplectic cone for manifolds with $b_2^+=1$ and Biran's ball packing theorem in dimension $4$. Along the way, we also show that these cohomologous symplectic forms can have distinct first Chern classes, which answers another question by Salamon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09550 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cohomologous symplectic forms with different Gromov widths Ning, Shengzhen Symplectic Geometry We study McDuff-Salamon's Problem 46 by showing that there exist closed manifolds of dimension $\geq 6$ admitting cohomologous symplectic forms with different Gromov widths. The examples are motivated by Ruan's early example of deformation inequivalent symplectic forms in dimension $6$ distinguished by Gromov-Witten invariants. To find cohomologous symplectic forms and compare their Gromov width, we make use of Li-Liu's theorem of symplectic cone for manifolds with $b_2^+=1$ and Biran's ball packing theorem in dimension $4$. Along the way, we also show that these cohomologous symplectic forms can have distinct first Chern classes, which answers another question by Salamon. |
| title | Cohomologous symplectic forms with different Gromov widths |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2505.09550 |