Spring 2012 Homotopy theory (MAS631)
Time: MWF 11:00-11:50
Lecture room: 2413
Instructor: Suhyoung Choi 4403(office) Office Hours:
schoi at math dot kaist dot ac dot kr Phone: 2732
We will go over the basic notions and the various tools of homotopy theory. These are treated by topics.
Many proofs will not be given but sometimes only be sketched.
We will center on fiber bundle theory. Topics:
fibrations, homotopy groups, Hurewicz map, obstruction theory, homology
with local coefficients,
postinikov systems, homotopy operations, homology of fiber spaces, spectral sequences.
Course book: G.W. Whitehead, Elements of homotopy theory
Grading: Midterm Exam (100pt) Final Presentation (150pt) Report (150pts) Attendance (50pts) Total 450pts
Course homepage: http://math.kaist.ac.kr/~schoi/Homotopy2011I.htm
| Monday |
Wednesday | Friday |
|||
| Feb 6 |
Introduction Section 1.1 | Feb 8 |
Section 1.2, 1.3 | Feb 10 |
Section 1.4 |
| Feb 13 |
Section 1.5 |
Feb 15 |
Section 1.6, 1.7 | Feb 17 |
Section 1.7 |
| Feb 20 |
Section 2.1 | Feb 22 |
Section 2.2 | Feb 24 |
Section 2.2 |
| Feb 27 |
Section 2.3 | Feb 29 |
Section 2.4, 2.5, 2.6 | March 2 |
Section 2.7 |
| March 5 |
Section 3.1, 3.2 | March 7 |
Section 3.3.3.4 | March 9 |
Section 3.5 |
| March 12 |
Section 3.6-3.8 | March 14 |
Section 4.1, 4.2 | March 16 |
Section 4.3, 4.4. |
| March 19 |
Section 4.5,4.6 | March 21 |
Section 4.7 | March 23 |
Section 4.8 |
| March 26 |
Midterm |
March 28 |
Midterm | March 30 |
Midterm |
| April 2 |
Section 4.9, 4.10 | April 4 |
Section 5.1 | April 6 |
Section 5.2,5.3 |
| April 9 |
Section 5.4,5.5 | April 11 |
Section 5.6 | April 13 |
Section 6.1 |
| April 16 |
Section 6.2 | April 18 |
Section 6.3 | April 20 |
Section 6.4 |
| April 23 |
Section 6.5 | April 25 |
Section 6.6 | April 27 |
Section 6.7 |
| April 30 |
Section 9.1, 9.2 | May 2 |
Section 9.3 | May 4 |
Section 9.4 |
| May 7 |
Section 9.5, 9.6 | May 9 |
Section 9.7 | May 11 |
Presentations |
| May 14 |
Presentations | May 16 |
Presentations | May 18 |
Presentations |
| May 21 |
Final |
May 23 |
Final | May 25 |
Final |
Final Presentation: Chapter 13. Homology of Fibre spaces
There will be three to 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 in the order given in the book. You have to markthe problems you did not solve.