Scattering manifolds and symplectic fillings

TL;DR

This paper explores the structure of scattering symplectic manifolds, showing they can be constructed by gluing weak symplectic fillings of contact manifolds, thus linking these concepts in symplectic geometry.

Contribution

It proves that all scattering symplectic manifolds are formed by gluing weak symplectic fillings, establishing a new connection between these geometric structures.

Findings

Scattering symplectic manifolds can be obtained by gluing weak symplectic fillings.

Pairs of weak symplectic fillings with matching boundaries can be glued to form scattering symplectic manifolds.

The paper provides a method to construct scattering symplectic manifolds from known fillings.

Abstract

Scattering symplectic manifolds are (closed) manifolds with a mildly degenerate Poisson structure. In particular they can be viewed as symplectic structures on a Lie algebroid which is almost everywhere isomorphic to the tangent bundle. In this paper we prove that all scattering symplectic manifolds arise as glueings of weak symplectic fillings of contact manifolds, and all pairs of weak symplectic fillings with matching boundaries can be glued to a scattering symplectic manifold.