E. Aldrovandi

A.A. 1997/98

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.