MATH 572: ALGEBRAIC
TOPOLOGY – Spring 2012
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Class |
week of |
Topics
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Suggested Problems |
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1 |
27/2 |
Free
products of groups. Seifert-van Kampen |
1.1:
8, 16, 17. 1.2: 2, 3, 4, 10, 19, 20,
21. |
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2 |
5/3 |
CW
complexes. Applications. |
0:
2, 6, 14, 16, 19, 20, 23. 1.2: 8, 9, 11, 12, 22. |
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3 |
12/3 |
Covering
Spaces. Classification. |
1.3:
4, 8, 9, 10, 12. |
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4 |
19/3 |
Deck
Transformations. Group Actions. |
1.3:
17, 20, 25, 27, 28, 30. |
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5 |
26/3 |
Simplicial and
singular homology. |
2.1: 5, 8, 12, 15, 17, 22, 29. |
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6 |
2/4 |
Homotopy invariance. Exact sequences. M1 |
2.2: 1, 4, 7, 12,
14. |
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7 |
9/4* |
Cellular
homology. Mayer-Vietoris 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. |
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10 |
30/4 |
Cohomology.
Universal coefficient theorem. |
3.1: 1, 5, 6, 8, 9, 11, 13. |
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11 |
7/5 |
Cup
product. Kunneth formula. |
3.2: 1, 3, 4, 5, 6, 7, 8, 9, 16, 18. |
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12 |
14/5 |
Orientation.
Poincare duality. |
3.3: 2, 4, 6, 7, 9, 11, 16, 25. |
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Instructors: Baris Coskunuzer,
Tolga Etgu, Burak Ozbagci |
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Grading Policy: 40% Midterm + 60% Final |
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Class Time: Tuesday 15:30 – 17:20 at CAS B34 |
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Discussion Session: Monday 11:00 – 12:15 at SCI 208 |
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Office Hours: Thursday 14:00 – 16:00 at SCI 104 |
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