When the Morse index is infinite

2004/03/31 by Alberto Abbondandolo, Pietro Majer
Mathematics · #math.DS #math.DG

paper · pdf

published as International Mathematics Research Notices 71 (2004) 3839-3854 · 10 pages

arxiv created 2004/03/31 · arxiv updated 2009/12/01

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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