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