Algebraic Topology II, Fall 2015
The course description can be found here. I'll put some suggested homework problems on this page. You should try to do all of them, but you only need to write up one or two per week.
Suggested homework.
- Week 1: Exercise on p193 of Hatcher, also 1, 2, 5, 6 on pp204-206.
- Week 2: pp204-206, numbers 7, 8, 9, 13.
- Week 4-5: p. 159, #38, pp228 1, 2, 7, 10, 18
- More on cohomology and cup products: p. 228ff #11, 12, 13.
- Manifolds and orientations: p. 257ff #1, 4, 6
- Cap products: Put a Delta-complex structure on the three-torus. Find a basis for the first cohomology with Z coefficients, as explicit simplicial cochains. Find a nontrivial 2-cycle, and compute cap products with the cohomology classes. Find the cap products of a fundamental cycle with the 1-cocycles.
- Poincare duality: We left a bunch of steps for exercises. These are mainly contained in p. 257ff #17, 30, 31, 35.
Other problems using Poincare duality: 24, 25, 26.
- A couple of cohomology of groups problems.
Jason Manning's home page.
Last Updated 2015-11-4