  Let f be a smooth Morse function on an infinite dimensional separable Hilbert
manifold, all of whose critical points have infinite Morse index and co-index.
For any critical point x choose an integer a(x) arbitrarily. Then there exists
a Riemannian structure on M such that the corresponding gradient flow of f has
the following property: for any pair of critical points x,y, the unstable
manifold of x and the stable manifold of y have a transverse intersection of
dimension a(x)-a(y).
