English

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.

Keywords

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

R2 v1 2026-06-23T06:28:29.568Z