Fibre Bundles pp 280-293 | Cite as

Characteristic Classes and Connections

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

Abstract

Apart from the previous chapter, the theory of fibre bundles in this book is a theory over an arbitrary space. Even the relation to manifolds in Chapter 18 is treated from a topological point of view, but in the context of smooth manifolds and vector bundles we can approach Chern classes using constructions from analysis. This idea, which goes back to a letter from A. Weil (see A. Weil Collected papers, Volume III, pages 422–36 and 571–574), involves choosing a connection or covariant derivative on the complex vector bundle, defining the curvature 2-form of the connection, and representing the characteristic class as closed 2q-form which is a polynomial in the curvature form. This proceedure is outlined in this chapter.

Keywords

Vector Bundle Smooth Manifold Cohomology Class Principal Bundle Curvature Form 
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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