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arXiv · 2506.06807

Unknottedness of symplectic submanifold fillings

Zhengyi Zhou
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Abstract

We show that any symplectic filling of the standard contact submanifold $(\mathbb{S}^{2n-1},\xi_{\mathrm{std}})$ of $(\mathbb{S}^{2n+1},\xi_{\mathrm{std}})$ in $(\mathbb{D}^{n+1},\omega_{\mathrm{std}})$ 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.

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Zhengyi Zhou. 2025-06-07. Unknottedness of symplectic submanifold fillings. https://arxiv.org/abs/2506.06807

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