Homotopy Theory of Lie groups and their Classifying Spaces

1. Lie groups, homomorphisms and linear representations. Irreducible representations. 2. Maximal tori in compact Lie groups. 3. Characters of representations. Ring of virtual characters. The Weyl theorem. 4. Actions of Lie groups. Homogeneous spaces (orbits) and equivariant maps. 5. Classifying spaces of topological groups and maps induced by homomorphisms. 6. Homotopy classification of maps between classifying spaces of discrete groups. 7. The Dwyer–Zabrodsky–Nottbohm theorem on homotopy classification of maps from the classifying spaces of p–toral groups to the classifying space of compact Lie groups. 8. Linear representations vs. homotopy representations of compact Lie groups.