The Tangent Bundle

Will J. Merry
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Will J. Merry: ETH Zürich, Departement Mathematik

Chapter Chapter 5 in Lectures on Differential Geometry I, 2026, pp 37-44 from Springer

Abstract: Abstract 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.

Date: 2026
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DOI: 10.1007/978-3-032-03733-6_5

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