Rational Homotopy Theory and Differential Forms

1. Introduction
Phillip Griffiths, John Morgan

2. Basic Concepts
Phillip Griffiths, John Morgan

3. CW Homology Theorem
Phillip Griffiths, John Morgan

4. The Whitehead Theorem and the Hurewicz Theorem
Phillip Griffiths, John Morgan

5. Spectral Sequence of a Fibration
Phillip Griffiths, John Morgan

6. Obstruction Theory
Phillip Griffiths, John Morgan

7. Eilenberg–MacLane Spaces, Cohomology, and Principal Fibrations
Phillip Griffiths, John Morgan

8. Postnikov Towers and Rational Homotopy Theory
Phillip Griffiths, John Morgan

9. deRham’s Theorem for Simplicial Complexes
Phillip Griffiths, John Morgan

10. Differential Graded Algebras
Phillip Griffiths, John Morgan

11. Homotopy Theory of DGAs
Phillip Griffiths, John Morgan

12. DGAs and Rational Homotopy Theory
Phillip Griffiths, John Morgan

13. The Fundamental Group
Phillip Griffiths, John Morgan

14. Examples and Computations
Phillip Griffiths, John Morgan

15. Functorality
Phillip Griffiths, John Morgan

16. The Hirsch Lemma
Phillip Griffiths, John Morgan

17. Quillen’s Work on Rational Homotopy Theory
Phillip Griffiths, John Morgan

18.
A

∞
-Structures and C

∞
-Structures
Phillip Griffiths, John Morgan

19. Exercises
Phillip Griffiths, John Morgan

Keywords: Mathematics, Algebraic Topology, Category Theory, Homological Algebra, Commutative Rings and Algebras, Topology, Algebra