Connections and Associated Bundles
IN this chapter we shall recast our previous machinery of connections, making more use of the fact that the connection and curvature forms take their values in the Lie algebra of the structure group. This will lead not only to a more systematic treatment of some topics that were previously handled in a rather ad hoc fashion, but also, in our following chapters, to generalizations of the Gauss–Bonnét–Poincare theorem and to closer contact with the machinery used in physics.
18.1. Forms with Values in a Lie Algebra
What do we mean by g—1dg?
18.1a. The Maurer-Cartan Form
If E is a vector bundle over ...