Definition:Tangent Bundle

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Definition

Let $M$ be a differentiable manifold.

Let $p \in M$ be a point in $M$.

Let $T_p M$ be the tangent space at $p$.


The tangent bundle of $M$ is the disjoint union of all the tangent spaces of $M$:

$\displaystyle T M = \coprod_{p \mathop \in M} T_p M$



Sources