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Cotangent space

In differential geometry, the cotangent space is a vector space associated with a point x {\displaystyle x} on a smooth (or differentiable) manifold M {\displaystyle {\mathcal {M}}} ; one can define a cotangent space for every point on a smooth manifold. Typically, the cotangent space, T x ∗ M {\displaystyle T_{x}^{*}\!{\mathcal {M}}} is defined as the…

Formal definitions, Properties & Exterior powers