nLab Differential Forms in Algebraic Topology

Contents

This entry collects material related to the book

on applications of differential forms, or rather of de Rham cohomology, in algebraic topology.

Related references:

Contents

1. 1 The de Rham complex on n\mathbb{R}^n

2. 2 The Mayer-Vietoris sequence

3. 3 Orientation and integration

4. 4 Poincaré lemma

5. 5 The Mayer-Vietoris argument

6. 6 The Thom isomorphism

7. 7 The Nonorientable case

8. 8 The Generalized Mayer-Vietoris Principle

9. 9 More Examples and Applications of the Mayer-Vietoris Principle

10. 10 Presheaves and Cech cohomology

11. 11 Sphere bundles

12. 13 Monodromy

13. 14 The spectral sequence of a filtered complex

14. 17 Review of homotopy theory

15. 19 Rational homotopy theory

16. 20 Chern Classes of a Complex Vector Bundle

17. 21 The Splitting Principle and Flag manifolds

18. 22 Pontrjagin classes

19. 23 The Search for the Universal Principal Bundle

category: reference

Last revised on January 28, 2024 at 06:53:47. See the history of this page for a list of all contributions to it.