Characteristic Classes

  • J. J. Duistermaat
Part of the Modern Birkhäuser Classics book series (MBC)


Let G be a Lie group with Lie algebra g and let P be a principal G-bundle over a manifold M, with projection π : PM. As in the paragraph preceding (6.8), let θ be a connection form in P, with curvature form Ω. We begin with the formulation in Theorem 13.1 of a basic result of André Weil [74], which states that there is a canonical homomorphism, which assigns to each conjugacy invariant polynomial on 9 a de Rham cohomology class of M, which, roughly speaking, is obtained by substituting the curvature form in the polynomial. The resulting cohomology classes in M are the characteristic classes in the title of this chapter.


Vector Bundle Cohomology Class Normal Bundle Chern Class Curvature Form 
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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • J. J. Duistermaat
    • 1
  1. 1.Mathematisch InstituutUniversiteit UtrechtUtrechtThe Netherlands

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