Cohomology Theory of Fibre Bundles. Characteristic Classes
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Characteristic classes We view characteristic classes as being defined by generators of the cohomology ring of the classifying space. Accordingly, we study the chohomology rings of the classifying spaces for the classical compact Lie groups and use their generators to define the Chern, Pontryagin and Stiefel-Whitney classes. Moreover, we discuss theWeil homomorphism, which provides a geometric description of characteristic classes in terms of de Rham cohomology, and genera of vector bundles. Finally, we explain a method to construct an approximation of the classifying space in terms of Eilenberg-MacLane spaces, known as the Postnikov tower.