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The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.

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Simple properties of the codifferential

To define $\star$ you need either a symplectic form or a Riemannian metric. Let us consider the first case. In this case, this isomorphism basically depends only on a symplectic form $\omega$. That is …
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