Fall 2010 Algebraic Topology

Time: Monday, Wednesday, Friday 3:00-4:00
Lecture room: 2413
Instructor: Suhyoung Choi 4403(office)
Office Hours:
schoi at math dot kaist dot ac dot kr Phone: 2732
% Send me e-mails if there are any questions.

Course book: Main: Topology and Geometry by Bredon, Springer Verlag,
Supplementary: Algebraic Topology by Hatcher, Cambridge

Topics: cohomology theory, Kunneth formula, products, Poincare duality

Grading: 4 Report (200pts) Attendance (50pts) Total 450pts
(If you do not attend classes more than five times, you will obtain an F.
If you do not turn in two reports or more, you will obtain an F. )

Course homepage: http://math.kaist.ac.kr/~schoi/topologyfall2010.html
The 4th report will replace the final exam.

9.1 week: Introduction, IV.6. Axioms of homology
9.6 week: V. 1-V.5. Differential forms
9.13 week: V.6. V.7. Cohomology
9.20 week: V.8, V.9. Cohomology
9.27 week: VI. 1. Products
10.4 week: VI.2. VI.3. Cohomology cross products
10.11 week: VI.4 Cup products
10.18 week: VI.5 Cap products
10.25 week: VI.5 Cap products
11.1 week: VI.6, VI.7 Orientation bundle
11.8 week: VI. Orientation bundle
11.15 week: VI.8 Duality
11.22 week: VI.9, VI.10 Duality on compact manifolds with boundary
11.29 week: VI.10, Applications VI.11 Intersection theory
12.6. week: VI.11, VI.12 Euler class, Lefschetz number, Vector fields
12.13. week: VI.12

There will be four reports. Their due dates will be posted here.
The scores of the late homework will be taken off by a formula.
1st report: (due October 27)
p. 264: 2, p.284: 1,3,5,7, p.291: 1,3,5
2nd report: (due November 17)
p.321: 1,2,3, p.326:1, p.334:1,3,6, p.338:2,3,4
3rd report: (due December 6)
p.348: 2, 3, p.355: 1, 3, 4, 6, 7, p.358: 1, 3, 5, p.366: 1, 3, 5
4th report: (due December 20)
p.377: 1, 4, p.378: 8, p.389: 1,3,4,7

Important Reminder: You need to solve in the order given in the book. You have to mark the problems you did not solve.