Fall 2023 Algebraic Topology II (MAS532)

Time: Monday, Wednesday 1:00-2:15
Lecture room: E2-1225
Instructor: Suhyoung Choi 4403(office)

Office Hours: TBA
email: schoixk at kaist dot ac dot kr Phone: 2732

The purpose of the course is to learn cohomology theory, including Kunneth formula, products, and Poincare duality.

This is an EDU-4.0 course. The lectures will be on the KLMS. The lecture notes will be on OneNote. We will distribute the links.
We will have discussions on sets of problems on Monday for the content of the week,
and the students will give presentations on Wednesday. The material to do will be posted before the beginning of the week.
You need to attend both classes, but we can end the classes earlier.

Course book: Main: Topology and Geometry by Bredon, Springer Verlag, (download from library.kaist.ac.kr)
                Supplementary: Algebraic Topology by Hatcher, Cambridge University Press (download from the site of the author),
                                             Singular homology theory by William S. Massey, Springer Verlag (download at library.kaist.ac.kr),
                                            Algebraic Topology by Edwin H. Spanier, Springer Verlag (download at library.kaist.ac.kr)

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

Grading:

Midterm exam (100pts), Final exam (100pts), Report (Oral (50 pts.) + Written (50pts.)), Attendance (50pts), Total 350pts

Exams will be offline Exams. Also, there will be presentations for reports done by groups. We will divide into groups of 2-3 students.

Schedule:
8.28 week: Introduction, IV.6-7, Axioms of homology, Degrees (Acyclic models, Direct limits)
9.4 week: V. 1-5 Differential forms
9.11 week: V.6. Cohomology
9.18 week: V.7.-V.8.Cohomology
9.25 week: V.9. Cohomology
10.2 week: IV. 16 The cross product, VI. 1. Products (up to Theorem 1.5)
10.9 week: VI. 1. Products (10.2 holiday)
10.16 week: The midterm exam period
10.23 week: VI.2.-3. Cohomology cross products,
10.30 week: VI.4 Cup products,
11.6 week: VI.5 Cap products
11.13 week: VI.6 VI.7. Orientation bundle
11.20 week: VI.7 Orientation bundle (KAIST enterance exam might be in this week)
11.27 week: VI.8 Duality theorems
12.4. week: VI.9 Duality on compact manifolds with boundary
12.11. week: The final exam period

Written presentations:
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.