Vector Bundles

  • Dale Husemoller
Part of the Graduate Texts in Mathematics book series (GTM, volume 20)

Abstract

A vector bundle is a bundle with an additional vector space structure on each fibre. The concept arose from the study of tangent vector fields to smooth geometric objects, e.g., spheres, projective spaces, and, more generally, manifolds. The vector bundle structure is so rich that the set of isomorphism classes of k-dimensional vector bundles over a paracompact space B is in a natural bijective correspondence with the set of homotopy classes of mappings of B into the Grassmann manifold of k-dimensional subspaces in infinite-dimensional space.

Keywords

Vector Bundle Open Covering Homotopy Class Finite Type Constant Rank 
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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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Dale Husemoller
    • 1
  1. 1.Department of MathematicsHaverford CollegeHaverfordUSA

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