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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.06807 |
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| _version_ | 1866913884744450048 |
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| author | Zhou, Zhengyi |
| author_facet | Zhou, Zhengyi |
| contents | We show that any symplectic filling of the standard contact submanifold $(\mathbb{S}^{2n-1},ξ_{\mathrm{std}})$ of $(\mathbb{S}^{2n+1},ξ_{\mathrm{std}})$ in $(\mathbb{D}^{n+1},ω_{\mathrm{std}})$ is smoothly unknotted if $n\ge 2$. We also give a self-contained proof of the Siefring intersection formula between punctured holomorphic curves and holomorphic hypersurfaces used in the proof using the $L$-simple setup of Bao-Honda. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06807 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unknottedness of symplectic submanifold fillings Zhou, Zhengyi Symplectic Geometry We show that any symplectic filling of the standard contact submanifold $(\mathbb{S}^{2n-1},ξ_{\mathrm{std}})$ of $(\mathbb{S}^{2n+1},ξ_{\mathrm{std}})$ in $(\mathbb{D}^{n+1},ω_{\mathrm{std}})$ is smoothly unknotted if $n\ge 2$. We also give a self-contained proof of the Siefring intersection formula between punctured holomorphic curves and holomorphic hypersurfaces used in the proof using the $L$-simple setup of Bao-Honda. |
| title | Unknottedness of symplectic submanifold fillings |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2506.06807 |