The Borel Conjecture and aspherical 4-manifolds

A space is aspherical if its universal cover is contractible.   Obstruction theory shows that any two aspherical CW complexes with isomorphic fundamental groups are homotopy equivalent.   The Borel Conjecture states that any two closed aspherical manifolds with isomorphic fundamental groups are homeomorphic.    The Borel Conjecture for manifolds with boundary states that two aspherical compact manifolds with isomorphic fundamental groups and homeomorphic boundaries are in fact homeomorphic.