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Vector Bundles

In: Differential Manifolds

Author

Listed:
  • Serge Lang

    (Yale University, Department of Mathematics)

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 [14].) 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.

Suggested Citation

  • Serge Lang, 1985. "Vector Bundles," Springer Books, in: Differential Manifolds, chapter 0, pages 41-60, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4684-0265-0_3
    DOI: 10.1007/978-1-4684-0265-0_3
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