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Lecture# Retractions vector fields and tangent bundles: Tangent bundles

Description

This lecture covers the concepts of retractions and tangent bundles on manifolds. It explains the definition of a retraction as a smooth map and the construction of the tangent bundle of a manifold. The lecture also discusses embedded submanifolds, defining functions, and the properties of tangent spaces. The instructor provides proofs and examples to illustrate the theoretical concepts.

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