Math 215c Notes

1. Smooth Manifolds: 4/7/15 1 2. The Tangent Bundle: 4/9/15 4 3. Parallelizability: 4/14/15 6 4. The Whitney Embedding Theorem: 4/16/15 8 5. Immersions, Submersions and Tubular Neighborhoods: 4/21/15 10 6. Cobordism: 4/23/15 12 7. Homotopy Theory: 4/28/15 14 8. The Pontryagin-Thom Theorem: 4/30/15 17 9. Differential Forms: 5/5/15 18 10. de Rham Cohomology, Integration of Differential Forms, and Stokes’ Theorem: 5/7/15 22 11. de Rham’s Theorem: 5/12/15 25 12. Curl and the Proof of de Rham’s Theorem: 5/14/15 28 13. Surjectivity of the Pontryagin-Thom Map: 5/19/15 30 14. The Intersection Product: 5/21/15 31 15. The Euler Class: 5/26/15 33 16. Morse Theory: 5/28/15 35 17. The h-Cobordism Theorem and the Generalized Poincaré Conjecture 37