symp-foliations

After Gromov published his '85 paper, pseudo-holomorphic curves have been one of the main tool in symplectic topology to prove “rigidity”.

Discussions related to holomorphic curves could be inspired by the following theorem in dimension 3.

Theorem (Novikov Reebless). Let M be a 3-manifold and let F be a Reebless foliation. Then

1. every leaf λ is π_1-injective; and
2. every transverse loop γ is essential in π_1.

Could something else be proved with holomorphic curves. Should one consider holomorphic curves in the leaves of the foliation? Should one do the symplectization of the foliated manifold to study holomorphic curves there like in an SFT-style?