MATH 572: ALGEBRAIC TOPOLOGY
Spring 2012
Class 
week of 
Topics 
Suggested Problems 
1 
27/2 
Free products of groups.
Seifertvan Kampen 
1.1:
8, 16, 17. 1.2: 2, 3, 4, 10, 19, 20, 21. 
2 
5/3 
CW complexes. Applications. 
0:
2, 6, 14, 16, 19, 20, 23. 1.2: 8, 9, 11, 12, 22. 
3 
12/3 
Covering Spaces. Classification. 
1.3:
4, 8, 9, 10, 12. 
4 
19/3 
Deck Transformations. Group
Actions. 
1.3:
17, 20, 25, 27, 28, 30. 
5 
26/3 
Simplicial and singular homology. 
2.1: 5, 8, 12, 15, 17, 22, 29. 
6 
2/4 
Homotopy invariance. Exact sequences. M1 
2.2: 1, 4, 7, 12, 14. 
7 
9/4* 
Cellular homology. MayerVietoris sequences. 
2.2: 15, 20, 21, 22, 29, 31, 33, 36. 
8 
16/4 
Homology with Coefficients. Hom. & fund. group 
2.2: 40, 41. 
9 
23/4 
Classical applications. 
2.B: 1, 2, 3, 5, 9, 10, 11. 
10 
30/4 
Cohomology. Universal coefficient theorem. 
3.1: 1, 5, 6, 8, 9, 11, 13. 
11 
7/5 
Cup product. Kunneth
formula. 
3.2: 1, 3, 4, 5, 6, 7, 8, 9, 16, 18. 
12 
14/5 
Orientation. Poincare duality. 
3.3: 2, 4, 6, 7, 9, 11, 16, 25. 
Instructors: Baris Coskunuzer,
Tolga Etgu, Burak Ozbagci 
