Characteristic Classes

Abstract

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 : P → M. 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.