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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Springer Book Archive