Time: Monday, Wednesday 10:30-11:45
Lecture room: 2412
Instructor: Suhyoung Choi 4403(office)
Office Hours:
email: schoi at math dot kaist dot ac dot kr Phone: 2732
% Send me e-mails if there are any questions.
The purpose of the course is to learn cohomology theory, including Kunneth formula, products, and Poincare duality.
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: Report (100pts.) Presentation (200pts.) Attendance (50pts.) Total 350pts.
(There will be no midterm or final. We will have presentations instead. For Presentations, I will assign problems or other things to be presented during the exam time. The report will be the write-up of the presentation.
The presentation will take place during the exam period or some other scheduled time.
)
Schedule:
9.2 week: Introduction, IV.6 Axioms of homology
9.9 week: V. 1-5 Differential forms
9.16 week: V.6. Cohomology
9.23 week: V.7. Cohomology
9.30 week: V.8.-V.9. Cohomology (presentation assignment on Wednesday)
10.7 week: V.9 Cohomology (Hangeul nal, holiday)
10.14 week: IV. 16 The cross product, VI. 1. Products
10.21 week: The midterm exam period (presentation, Wednesday 9:00-11:45)
10.28 week: VI. 1. Products , VI.2.-3. Cohomology cross products,
11.4 week: VI.4 Cup products,
11.11 week: VI.5 Cap products
11.18 week: VI.6 VI.7. Orientation bundle (presentation assignment on Wednesday)
11.25 week: VI.7 Orientation bundle (KAIST enterance exam 27, 28)
12.2 week: VI.8 Duality theorems, presentation
12.9. week: VI.9 Duality on compact manifolds with boundary, presentation
12.16. week:The final exam period ( presentation, Wednesday 9:00-11:45)
From 12.2 Student will give presentations.
Reports:
These will be submitted to the KLMS.
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.