I'm stuck on the following problem: let $S$ be a compact orientable hypersurface in the symplectic manifold $(M,\omega)$. Prove that there exists a smooth function $H: M \to \mathbb R$ such that $0$ is a regular value of $H$ and $S \subset H^{-1}(0)$.
Since $S$ and $M$ are orientable, I can find a tubular neighborhood $N\simeq S \times (-\epsilon, \epsilon)$, which is open in $M$ and with $S$ corresponding to $S \times \{0\}$. Then $S$ is the inverse image of the regular value 0 under the projection onto the second factor $N \to (-\epsilon,\epsilon)$. Is there a clean way to see that I can extend this map to all of $M$ such that 0 remains a regular value?