Computational Geometry
The Morse Lemma is a fundamental result in Morse theory, stating that if a function has a non-degenerate critical point, then in a neighborhood of that point, the function can be expressed in a specific simplified form. This lemma provides a way to understand the local behavior of functions and their critical points, allowing one to analyze the topology of manifolds based on these features. It connects critical points to the geometry of the function, revealing important information about the manifold's structure.
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