Removing a ray from a noncompact symplectic manifold

Abstract

We prove that any noncompact symplectic manifold which admits a properly embedded ray with a wide neighborhood is symplectomorphic to the complement of the ray by constructing an explicit symplectomorphism in the case of the standard Euclidean space. We use this excision trick to construct a nowhere vanishing Liouville vector fields on every cotangent bundle.

15 pages, 5 figures. Added figures and an application in Section 4