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We begin this chapter by defining the cotangent space of a manifold. We then move onto the tangent and cotangent bundles. We conclude by recalling the Euclidean versions of the Inverse and Implicit Function Theorems, and generalising the Inverse Function Theorem to manifolds. In the next chapter we will generalise the Implicit Function Theorem to manifolds.

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The Tangent Bundle

  • 章节

  • 发表日期：

    2026年

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  • Will J. Merry

摘要

We begin this chapter by defining the cotangent space of a manifold. We then move onto the tangent and cotangent bundles. We conclude by recalling the Euclidean versions of the Inverse and Implicit Function Theorems, and generalising the Inverse Function Theorem to manifolds. In the next chapter we will generalise the Implicit Function Theorem to manifolds.