A Examples of application of transversality of submanifolds

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Hi,
I am a PhD student, I work on transversal submanifolds. I want to know if someone has an example of application of transversality in physics or ingenning or in any other area, I hear that there is an application in construction of plans but I didn't find it.
Thank you in advance.
 
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Thread 'Injective immersion and embedding'

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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