Elementary Differential Topology
The Morse Lemma is a fundamental result in differential topology that provides a way to analyze the local behavior of Morse functions around their critical points. It states that, under certain conditions, near any non-degenerate critical point, a Morse function can be expressed as a quadratic function in the local coordinates. This lemma is essential for understanding how critical points influence the topology of manifolds and connects to various applications in both Morse theory and CW complex structures.
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