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Vector Bundles

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Part of the Graduate Texts in Mathematics book series (GTM,volume 160)

Abstract

The collection of tangent spaces can be glued together to give a manifold with a natural projection, thus giving rise to the tangent bundle. The general glueing procedure can be used to construct more general objects known as vector bundles, which give powerful invariants of a given manifold. (For an interesting theorem see Mazur [Maz 61].) In this chapter, we develop purely formally certain functorial constructions having to do with vector bundles. In the chapters on differential forms and Riemannian metrics, we shall discuss in greater detail the constructions associated with multilinear alternating forms, and symmetric positive definite forms.

Keywords

  • Banach Space
  • Exact Sequence
  • Vector Bundle
  • Commutative Diagram
  • Tangent Bundle

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1995 Springer-Verlag New York, Inc.

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Lang, S. (1995). Vector Bundles. In: Lang, S. (eds) Differential and Riemannian Manifolds. Graduate Texts in Mathematics, vol 160. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4182-9_3

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  • DOI: https://doi.org/10.1007/978-1-4612-4182-9_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8688-2

  • Online ISBN: 978-1-4612-4182-9

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