We introduce scattering-symplectic manifolds, manifolds with a type of minimally
degenerate Poisson structure that is not too restrictive so as to have a large class of
examples, yet restrictive enough for standard Poisson invariants to be computable.
This paper will demonstrate the potential of the scattering symplectic setting. In
particular, we construct scattering-symplectic spheres and scattering symplectic
gluings between strong convex symplectic fillings of a contact manifold. By
giving an explicit computation of the Poisson cohomology of a scattering
symplectic manifold, we also introduce a new method of computing Poisson
cohomology.
