内容

目次

1. Introduction; 2. The alternating algebra; 3. De Rham cohomology; 4.Chain complexes and their cohomology; 5. The Mayer-Vietoris sequence; 6.Homotopy; 7. Applications of De Rham cohomology; 8. Smooth manifolds; 9.Differential forms on smooth manifolds; 10. Integration on manifolds; 11.Degree, linking numbers and index of vector fields; 12. The Poincare-Hopftheorem; 13. Poincare duality; 14. The complex projective space CPn; 15.Fiber bundles and vector bundles; 16. Operations on vector bundles and theirsections; 17. Connections and curvature; 18. Characteristic classes ofcomplex vector bundles; 19. The Euler class; 20. Cohomology of projective andGrassmanian bundles; 21. Thom isomorphism and the general Gauss-Bonnetformula.