Unknottedness of symplectic submanifold fillings

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.