symp-foliations

(R.L. Fernandes, F. Presas, G. Meigniez) Conjecture: Let M be a closed, odd-dimensional, simply–connected manifold. Then it does not admit a codimension-1 strong symplectic foliation. It is known by work of Mitsumatsu that the 5-sphere does admit a weak symplectic foliation. In dimension 3, the conjecture is true due to Novikov's theorem.

(A. Mori) Conjecture: Let (M,F) be a codimension-1 oriented foliation on a closed odd dimensional manifold. If the space of leafwise closed non-degenerate 2-forms is non-empty and contains no closed forms, there exists a closed leaf.

(M. Bertelson, G. Meigniez) Is there an analogue of Thurston's h–principle for symplectic foliations of codimension higher than 1?