Removing a ray from a noncompact symplectic manifold
Symplectic Geometry
2019-03-12 v2 Differential Geometry
Dynamical Systems
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.
Cite
@article{arxiv.1812.00444,
title = {Removing a ray from a noncompact symplectic manifold},
author = {Xiudi Tang},
journal= {arXiv preprint arXiv:1812.00444},
year = {2019}
}
Comments
15 pages, 5 figures. Added figures and an application in Section 4