General Theory of Characteristic Classes
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.
KeywordsVector Bundle Line Bundle Characteristic Classis Chern Class Euler Class
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