Tangent Bundle
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In topology, a tangent bundle of a given manifold is a new manifold that consists of the tangent spaces for each point pasted together in a continuous fashion.
Tangent bundle is a graduate-level concept that would be first encountered in a differential geometry course.
Prerequisites
| Manifold: | A manifold is a topological space that is locally Euclidean, i.e., around every point, there is a neighborhood that is topologically the same as an open unit ball in some dimension. |
| Tangent Space: | A tangent space is a vector space of all possible tangent vectors to a point on a manifold. |
| Topology: | (1) As a branch of mathematics, topology is the mathematical study of object's properties that are preserved through deformations, twistings, and stretchings. (2) As a set, a topology is a set along with a collection of subsets that satisfy several defining properties. |