  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.

Symplectic Geometry;Differential Geometry