Fall 2012 Algebraic Topology
Time: Monday, Wednesday, Friday 3:00-4:00
Lecture room: 2412
Instructor: Suhyoung Choi 4403(office)
TA: K. Choi 4423
Office Hours:
email: 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/topologyfall2012.html
The reports will replace the midterm and final exams.
Schedule:
9.3 week: Introduction, IV.6 Axioms of homology
9.10 week: V. 1-5 Differential forms (W, F: lecturer)
9.17 week: V.6. Cohomology
9.24 week: V.7. Cohomology (lecturer)
10.1 week: V.8. Cohomology (M, W: holidays)
10.8 week: V.9. Cohomology
10.15 week: IV. 16 The cross product, VI. 1. Products (lecturer)
10. 22 week: The midterm exam period
10.29 week: VI. 1. Products , VI.2.-3. Cohomology cross products,
11.5 week: VI.4 Cup products,
11.12 week: VI.5 Cap products
11.19 week: VI.6 VI.7. Orientation bundle
11.26 week: VI.7 Orientation bundle VI.8 Duality theorems
11.29 week: VI.8 Duality theorems, VI.9 Duality on compact manifolds with boundary
12.3. week: VI.10, Applications
12.10. week: Reports on VI 11, 12
12. 17. week: The final exam period
Reports:
There will be about four reports. Their due dates will be posted here.
The scores of the late homework will be taken off by a formula.
Important Reminder: You need to solve problems in the order given in the book. You have to mark the problems you did not solve.
Turn in the home work to TA K. Choi.
HW 1. P 190: 3, P. 194: 3, P. 264: 1,2, P. 284: 2, P. 285: 4, 5 (Due Oct. 12)
HW 2. P. 291: 1, 5, P. 321: 2, 3, P. 326: 1, P. 334: 3, 4, 6, P. 338: 2, 3 (Due Nov. 30)
HW 3. P. 348: 2, P. 355: 3, 4, 7, P. 358: 2, P. 359: 5 (Due Dec. 17)
Report presentations: 12/10, 12/12, 12/14 (2 hours 15:00-17:00), 12/19
Sections VI 11, 12