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When the Morse index is infinite

Alberto Abbondandolo·Pietro Majer
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Abstract

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).

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Alberto Abbondandolo, Pietro Majer. 2004-03-31. When the Morse index is infinite. https://arxiv.org/abs/math/0403552

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