I Morse Theory & Lagrangian Mechanics: Is There a Connection?

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I read somewhere that Morse originally applied his theory to the calculus of variations. I'm wondering, is this application useful in physics and mechanics, like maybe it sheds light on lagrangian mechanics? Does anyone know?
 
Hello! There is a simple line in the textbook. If ##S## is a manifold, an injectively immersed submanifold ##M## of ##S## is embedded if and only if ##M## is locally closed in ##S##. Recall the definition. M is locally closed if for each point ##x\in M## there open ##U\subset S## such that ##M\cap U## is closed in ##U##. Embedding to injective immesion is simple. The opposite direction is hard. Suppose I have ##N## as source manifold and ##f:N\rightarrow S## is the injective...
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