Learning Seminar on Cohomology
Matteus Froese are co-organizing this seminar because we 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—2:20, 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. 113–121) |
| September 29 | Harper Niergarth and Mike Cummings | 2.1 More on excision (p. 121–124) |
| October 6 | Matteus Froese | 2.1 A couple applications and naturality of excision; equivalence of simplicial and singular homology (p. 126–131) |
| October 13 | — | no seminar on account of reading week |
| October 20 | Mike Cummings | 2.2 Degree and cellular homology (p. 134–141) |
| October 27 | Harper Niergarth | 2.2 Examples of cellular homology (p. 141–142), Mayer-Vietories (p. 149-151), homology with coefficients (p. 153-154) |
| November 3 | Abdullah Zubair | 3.1 Cohomology groups; universal coefficient theorem (p. 190–197) |
| November 10 | Matteus Froese | 3.1 Cohomology of spaces (p. 197–204) |
| November 17 | Mike Cummings | 3.2 Cup product (p. 206–214) |
| November 24 | 3.2 More on cup products (p. 214–221) | |
| December 1 | 3.3 Orientations and homology, Poincaré duality | |
| December 8 | 3.3 Connection between duality and the cup product; other forms of duality | |
| December 15 | buffer/overflow, or 3.F Limits and Ext |