Near the top of the second page of [this paper][1], it is claimed that if two 4-manifolds $X,Y$ are homeomorphic, then their producs $X \times X, Y \times Y$ are diffeomorphic. Why is this true? It is trivially correct for 2-manifolds and lower dimensions. Is it also correct for 3-manifolds? What about higher dimensions?

References would be greatly appreciated as well.


  [1]: http://arxiv.org/abs/math/0012096 "Ivan Smith: On moduli spaces of symplectic forms, 2000"