Learning Seminar on Cohomology
Matteus Froese and I want to know: What is cohomology? How do you compute it? What do you do with it? In this seminar, we will aim to answer these questions and more.
Please join us if you are interested, and let me know if you'd like to join the mailing list.
- Tuesdays 1:00—2:30, in MC 6029
Main reference
Schedule
This is our tentative plan; it will be updated as needed. Sections and page numbers refer to Hatcher.
| Date | Speaker | Topics |
|---|---|---|
| September 8 | Mike Cummings | 2.1 Δ-complexes and simplicial homology (p. 97–107) |
| September 15 | Matteus Froese | 2.1 Singular homology and homotopy invariance (p. 108–113) |
| September 22 | Harper Niergarth | 2.1 Exact sequences (briefly) and excision (p. 113–122ish) |
| September 29 | 2.1 More on excision (p. 122–128) | |
| October 6 | 2.1 Equivalence of simplicial and singular homology (p. 128–131) | |
| October 13 (reading week) | 2.2 Degree and cellular homology (p. 134–141) | |
| October 20 | 2.2 More on cellular homology (p. 142–149) | |
| October 27 | 3.1 Cohomology groups; universal coefficient theorem (p. 190–197) | |
| November 3 | 3.1 Cohomology of spaces (p. 197–204) | |
| November 10 | 3.2 Cup product | |
| November 17 | 3.2 More on cup products | |
| November 24 | 3.3 Orientations and homology, Poincaré duality | |
| December 1 | 3.3 Connection between duality and the cup product; other forms of duality | |
| December 8 | 3.F Limits and Ext | |
| December 15 | buffer/overflow week |