Symplectic, Poisson, and contact geometry on scattering manifolds

TL;DR

This paper introduces scattering-symplectic manifolds, a new class with a specific Poisson structure, demonstrating their properties, examples, and a novel method for computing Poisson cohomology.

Contribution

It defines scattering-symplectic manifolds, constructs explicit examples, and develops a new approach for calculating Poisson cohomology.

Findings

Construction of scattering-symplectic spheres

Gluing techniques for symplectic fillings

Explicit Poisson cohomology computation method

Abstract

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.