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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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Is there any intrinsic ( without any reference to embedding ) and coordinate free , basis fr... [duplicate]

Is there any way to uniquely characterise manifolds ( their geometrical and topological properties) without refering to charts or to a particular hyperspace containing the manifold. For example could …
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