Is it true that every orientable surface bundle can be made into a symplectic fibration?If yes, why?


What about the particular case that $M$ is a connected compact 4-manifold?



Orientable surface bundle
This is a consquence of a theorem of THurston on the existence of symplectic fibrations.


See page 6 here for a proof.


<https://pdfs.semanticscholar.org/9c1a/c1ff4ccb03aab1633c1a6f97458b7054d9e4.pdf>


