On differentiable functions with isolated critical points

摘要: THE PURPOSE of this paper is to describe some quantitative aspects a Morse theory for differentiable functions on manifold which have only isolated but possibly degenerate critical points. We will show that around such points locally, function splits into and non-degenerate parts, in terms the relative homology can be expressed certain way when passing level. Our investigation originated connection with specific geometric problem, namely prove existence infinitely many geometrically distinct periodic geodesics very large class compact riemannian manifolds, see [3], results may useful other applications as well. wish thank Ralph Abraham Alan Weinstein helpful conversations.