Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 146 / 4 / a / Solution

The symplectic neighborhood theorem says that a neighborhood of a compact symplectic submanifold is determined, up to symplectomorphism, by the restricted symplectic form and its symplectic normal bundle. More precisely, if $f:S_0\to S_1$ is a symplectomorphism and an isomorphism of symplectic normal bundles covers $f$, then that bundle isomorphism extends to a symplectomorphism between neighborhoods of $S_0$ and $S_1$.