Course Syllabus
The official course plan is here.
Main topics:
- smooth manifolds and smooth maps
- tangent bundles, immersions, submersions, embeddings
- Sard's theorem, immersions and embeddings of manifolds into Euclidean space
- Transversality
- Intersection theory, mod-2 and integrally
- Applications (Jordan-Brouwer theorem, Borsuk-Ulam theorem)
- Lefschetz fixed point theorem, Euler characteristic, Hopf degree theorem
- Either: Introduction to Morse theory
- Or: The topology of Lie groups
A more detailed plan will appear at a later stage.
Course Summary:
| Date | Details | Due |
|---|---|---|
| Tue Jan 26, 2021 | Assignment Problem set 1 | due by 12pm |
| Tue Feb 2, 2021 | Assignment Problem set 2 | due by 12pm |
| Tue Feb 9, 2021 | Assignment Problem set 3 | due by 12pm |
| Tue Feb 16, 2021 | Assignment Problem set 4 | due by 12pm |
| Tue Feb 23, 2021 | Assignment Problem set 5 | due by 12pm |
| Tue Mar 2, 2021 | Assignment Problem set 6 | due by 12pm |
| Tue Mar 23, 2021 | Assignment Problem set 7 | due by 12pm |
| Tue Apr 13, 2021 | Assignment Problem set 8 | due by 12pm |
| Tue Apr 20, 2021 | Assignment Problem set 9 | due by 12pm |
| Tue Apr 27, 2021 | Assignment Problem set 10 | due by 12pm |
| Tue May 11, 2021 | Assignment Problem set 11 | due by 12pm |
| Tue May 18, 2021 | Assignment Problem set 12 | due by 12pm |