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Mathematical discipline which studies some properties of smooth manifolds, which allow to generalize calculus to beyond $\mathbb{R}^n$. General relativity is written in this language.

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How prove that the 2-form of the hamiltonian formalism is a sympletic form?

The form What I say is $$\omega= dp_{\mu}\land dq^{\mu} $$ (I wrote anyway because the question is quick) how prove that are sympletic, i prove that $$d\omega=0$$but how prove that this is non-degen …