Poisson geometry in dimension 2 and symplectic geometry in dimension 4

From CRCG-Wiki

A groupoid with a multiplicative structure can be roughly understood as a manifold with local symmetries which preserve the structure. In particular, one may expect to find interesting symplectic manifolds among symplectic integrations. We support this point of view by describing some properties of the 4-dimensional integrations of topologically stable Poisson structures on surfaces.