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.

27 pages, comments welcome!