Abstract
This chapter explains how the curvatures of connections can be used to construct De Rham cohomology classes that distinguish isomorphism classes of vector bundles and principal bundles. These classes are known as characteristic classes. The discussions cover the Bianchi Identity; characteristic forms; characteristic classes for complex vector bundles and the Chern classes; characteristic classes for real vector bundles and the Pontryagin classes; examples of bundles with nonzero Chern classes; The degree of the map g → gm from SU(2) to itself; and a Chern-Simons form.
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