Program:

• Principal G-bundles, Connections, Chern-Weil homomorphism;
• De Rham Theorem (after A. Weil);
• Some homological algebra:
  • Nerves;
  • Double complexes;
  • Simplicial methods;
• Topological theory:
  • Characteristic classes for topological principal fiber bundles, classifying spaces;
  • De Rham and Chern-Weil for simplicial manifolds and principal bundles, simplicial construction of the universal bundle

• Application to the classical groups: Chern, Pontrjagin, Euler classes;
• Application to flat bundles, secondary classes.