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Ch. 1. Introduction -- Ch. 2. The Alternating Algebra -- Ch. 3. de Rham Cohomology -- Ch. 4. Chain Complexes and their Cohomology -- Ch. 5. The Mayer-Vietoris Sequence -- Ch. 6. Homotopy -- Ch. 7. Applications of de Rham Cohomology -- Ch. 8. Smooth Manifolds -- Ch. 9. Differential Forms on Smooth Manifolds -- Ch. 10. Integration on Manifolds -- Ch. 11. Degree, Linking Numbers and Index of Vector Fields -- Ch. 12. The Poincare-Hopf Theorem -- Ch. 13. Poincare Duality -- Ch. 14. The Complex Projective Space CP n -- Ch. 15. Fiber Bundles and Vector Bundles -- Ch. 16. Operations on Vector Bundles and their Sections -- Ch. 17. Connections and Curvature -- Ch. 18. Characteristic Classes of Complex Vector Bundles -- Ch. 19. The Euler Class -- Ch. 20. Cohomology of Projective and Grassmannian Bundles -- Ch. 21. Thom Isomorphism and the General Gauss-Bonnet Formula -- App. A. Smooth Partition of Unity -- App. B. Invariant Polynomials -- App. C. Proof of Lemmas 12.12 and 12.13 -- App. D. Exercises

Characteristic classes --- Classes caractéristiques --- Formes différentielles --- 514.74 --- Algebraic and analytic methods in geometry --- Characteristic classes. --- 514.74 Algebraic and analytic methods in geometry --- Classes caractéristiques --- Formes différentielles --- Differential forms --- Homology theory --- Cohomology theory --- Contrahomology theory --- Algebraic topology --- Forms, Differential --- Continuous groups --- Geometry, Differential --- Classes, Characteristic --- Differential topology --- Differential forms. --- Homology theory. --- Homologie --- Variétés différentiables --- Topologie differentielle --- Analyse sur une variété --- Classes et nombres caracteristiques

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Algebraic topology