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From Calculus to Cohomology by Madsen
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Jump to navigationJump to searchFrom Calculus to Cohomology: De Rham Cohomology and Characteristic Classes by Ib H. Madsen
Table of Contents
- 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 Poincaré-Hopf theorem
- 13. Poincaré duality
- 14. The complex projective space $CP^n$
- 15. Fiber bundles and vector bundles
- 16. Operations on vector bundles and their sections
- 17. Connections and curvature
- 18. Characteristic classes of complex vector bundles
- 19. The Euler class
- 20. Cohomology of projective and Grassmanian bundles
- 21. Thom isomorphism and the general Gauss-Bonnet formula.