Non-singular graph-manifolds of dimension 4
  A compact 4-dimensional manifold is a non-singular graph-manifold if it can be obtained by the glueing T^2-bundles over compact surfaces (with boundary) of negative Euler characteristics. If none of glueing diffeomorphisms respect the bundle structures, the graph-structure is called reduced. We prove that any homotopy equivalence of closed oriented 4-manifolds with reduced nonsingular graph-structures is homotopic to a diffeomorphism preserving the structures. 
A. Mozgova