Topological Proof of Cartan’s Theorem

Abstract

We will give another proof of Cartan’s Theorem 16.5. Since this was already proved in the last chapter, the reader can skip this chapter with no loss of continuity. As a by-product of this second proof, we will obtain some topological insight into the “flag manifold” G/T, where T is a maximal torus in the compact Lie group T, a topic that we will take up in the final chapter.