Topics and Exercises

Week	Topics
1	Introduction to cohomology, Universal coefficient theorem for cohomology
2	Cohomology of spaces, applications of Universal coefficient theorem
3	Cellular cohomology, cup product, cohomology rings of RP^2 and T^2
4	Graded commutativity of cup product, tensor product of graded rings, Kunneth theorem
5	Proof of Kunneth theorem, cohomology of real projective space
6	Cohomology of projective spaces, applications, Manifolds and orientations
7	Fundamental class of an oriented closed manifold, cap product
8	Relative cap product, cohomology with compact supports, direct limits, PD map
9	Proof of Poincare duality, application to Euler characteristic
10	More applications of PD: recognizing manifolds, middle-dimensional bilinear forms, Lefschetz duality

Exercises:

Exam from MA3H60

Exercises for Week 1

Exercises for Week 2

Exercises for Week 3

Exercises for Week 4

Exercises for Week 5

Exercises for Week 6

Exercises for Week 7

Exercises for Week 8

Exercises for Week 9

Exercises for Week 10