We consider geometric decompositions of aspherical 4-manifolds which fibre over 2-orbifolds. We show that no such manifold admits infinitely many fibrations over hyperbolic base orbifolds and that “most” Seifert fibred 4-manifolds over hyperbolic bases have a decomposition induced from a decomposition of the base.
"Geometric decompositions of 4-dimensional orbifold bundles." J. Math. Soc. Japan 63 (3) 871 - 886, July, 2011. https://doi.org/10.2969/jmsj/06330871