On Homotopic Equivalence of Fibering into Tori and Total Space. Case of Nonempty Boundary - Mozgova, A. A. (Ukrains’kyi Matematychnyi Zhurnal, 2002)
We present a criterion that indicates the case where a smooth compact 4-manifold with irreducible boundary is homotopically equivalent to the total space of a fibering into two-dimensional closed aspherical surfaces over a two-dimensional aspherical surface with boundary.