Cotangent Space

The Cotangent Space at a point $p$ in a differentiable manifold $M$ is the dual space to the Tangent Space $T_pM$. It is denoted by $T_p^M$ or $T_p^(M)$.

The Cotangent Space $T_p^*M$ is composed of all linear maps that map from $T_pM$ to the real numbers. As such, elements of the cotangent space are often viewed as differential 1-forms.

The collection of all cotangent spaces at every point in the manifold forms the Cotangent Bundle $T^*M$, a concept central to differential forms and symplectic geometry.

See also


Topics in Topological Data Analysis

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