Cohomological properties of ruled symplectic structures

This survey presents some recent results by the authors and Polterovich on the topological properties of ruled symplectic manifolds. The bundle M \to P \to B that is associated with a ruled manifold has the group of Hamiltonian symplectomorphisms of M as structure group if the base is simply connected. Thus information about Hamiltonian bundles gives stability results for ruled structures as well as obstructions to their existence.