Given an arbitrary Hilbert manifold, can on find a complete Riemannian metric and a Morse function satisfying the Palais-Smale condition?



existence of Morse functions satisfying the Palais-Smale condition
I recently learned that the answer to the question is YES, answered in the ETH preprint "H-cobordism for Hilbert Manifolds" by Dan Burghelea. I found the reference in the article "On the differential topology of Hilbert manifolds" of Eells and Elworthy.


