Abstract:
To give positive results of the equivalence, we construct symplectomorphisms between noncompact symplectic (ncsp) manifolds.
First, we consider a ncsp manifold with different symplectic forms.
We prove that a cohomologuous smooth path of symplectic forms are related by an isotopy of symplectomorphisms, provided that the path has bounded log-variation and the ends of the manifold are topologically tame with trivial 1st cohomology.
This is an analogy of Moser stability for compact symplectic manifolds.
Second, we consider different open submanifolds of a ncsp manifold.
We prove that the complement of a properly embedded ray is symplectomorphic to the ambient ncsp manifold, and explain the constructions in detail.
