Morse Theory and Critical Groups

Abstract

Let H be a Hilbert space with inner product $(\cdot ,\cdot )_H$ and let $\varphi \in C^2(H)$. By $\varphi '(\cdot )$ we denote the Fréchet derivative of $\varphi$ and by $\nabla \varphi (\cdot )$ its gradient, that is, $\nabla \varphi (u)\in H$ for every $u\in H$ and.

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