Surface bundles over circles and surfaces have been and continue to be well studied. The main focus of this thesis is manifolds which admit multiple surface bundle structures over low-dimensional manifolds. In [Sal15], Salter proved certain cohomological properties of 4-manifolds with multiple surface bundle structures over surfaces. In this thesis, we will analyze the extent to which analogous results are true in other dimensions as well as construct examples of spaces with multiple

Symplectic 4-manifolds are coarsely classified by Kodaira dimension; those of Kodaira dimension 0 are characterized by torsion canonical class. A symplectic Calabi-Yau 4-manifold (SCY) is a symplectic 4-manifold with trivial canonical class. SCYs satisfy strict homological constraints: the (virtual) first Betti number is 0, 2, 3, or 4. The fundamental group of an SCY satisfies the same constraints and is called an SCY group. A symplectic manifold is almost complex and so admits a canonical spin^c structure, permitting access to Seiberg-Witten theory by which it is shown that linear SCY groups with virtual first Betti number 4 are virtually solvable and hence elementary amenable; Hirsch length calculations force such a group to be virtually Z^4.