Fibre Bundles pp 294-311 | Cite as

General Theory of Characteristic Classes

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

Abstract

Using vector bundles over a space X, we are able to associate with X various sets which reflect some of the topological properties of X, for example, Vect F (X), the semigroup of isomorphism classes of F-vector bundles; Vect F n (X), the set of isomorphism classes of n-dimensional vector bundles over X; and K F (X), the group completion of Vect F (X). We view a characteristic class as a morphism defined on one of the cofunctors Vect F , Vect F n , or K F with values in a cohomology cofunctor. In several important cases, we are able to give a complete description of all characteristic classes. We conclude with a discussion of properties of the Chern character.

Keywords

Vector Bundle Line Bundle Characteristic Classis Chern Class Euler Class 
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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