Manifolds with Poly-Surface Fundamental Groups

We study closed topological 2n-dimensional manifolds M with poly-surface fundamental groups. We prove that if M is simple homotopy equivalent to the total space E of a Y-bundle over a closed aspherical surface, where Y is a closed aspherical n-manifold, then M is s-cobordant to E. This extends a well-known 4-dimensional result of Hillman in 14] to higher dimensions. Our proof is different from that of the quoted paper: we use Mayer-Vietoris techniques and the properties of the -theory assembly maps for such bundles.