symp-foliations

What is the precise foliated analogue of Gromov's compactness for symplectic foliations?. Energy bounds seem to require strongness. Can pseudoholomorphic curve techniques still be carried out in the weak setting? Pancholi and Venugopalan have proven an analogue of McDuff's classification result of ruled symplectic 4-manifolds.

It is straightforward to define what a symplectic filling is for a contact foliation. Is it possible to develop an analogue of the Weinstein cobordism theory? Morse theory for foliations is already very poorly understood, so it seems difficult.

Every codimension-1 strong symplectic foliation has an associated line field, its kernel. This depends only on the global closed 2-form and not on the foliation itself. Still, are there any meaningful dynamics to be studied? Remark: a strong symplectic foliation is stable Hamiltonian only if the foliation 1-form is closed and therefore essentially a mapping torus.