Removing parametrized rays symplectically

Extracting isolated rays from a symplectic manifold result in a manifold symplectomorphic to the initial one. The same holds for higher dimensional parametrized rays under an additional condition. More precisely, let $(M,ω)$ be a symplectic manifold. Let $[0,\infty)\times Q\subset\mathbb{R}\times Q$ be considered as parametrized rays $[0,\infty)$ and let $φ:[-1,\infty)\times Q\to M$ be an injective, proper, continuous map immersive on $(-1,\infty)\times Q$. If for the standard vector field $\frac{\partial}{\partial t}$ on $\mathbb{R}$ and any further vector field $ν$ tangent to $(-1,\infty)\times Q$ the equation $φ^*ω(\frac{\partial}{\partial t},ν)=0$ holds then $M$ and $M\setminus φ([0,\infty)\times Q)$ are symplectomorphic.

No reviews yet.

No comments yet.