Department Syllabus
MAT 215A: Topology
| When taught: |
Fall, alternate years |
| Suggested text ($): |
Algebraic Topology, Allen Hatcher, Cambridge Univ, ISBN 10:0521795400 ($30), Dmitry Fuchs' handouts |
| Units/lectures: |
4 units; lecture/term paper or discussion section |
| Prerequisites: |
Graduate standing or consent of instructor. |
Catalog description
Fundamental group and covering space theory. Homology and cohomology. Manifolds and duality. CW complexes. Fixed point theorems.
Suggested schedule
| Prepared by: |
Dmitry Fuchs, Greg Kuperberg |
| Posted: |
May 2009 |
| Lectures | Sections |
Topics/Comments |
|---|
| Week 1 | Ch. 0 |
Examples of topological spaces and constructions |
| Week 2 | Sec. 1.1 |
(Path) connected spaces, homotopy, retracts
|
| Week 3 | Ch. 1.1 |
Simply connected spaces, fundamental groups
|
| Week 4 | Ch. 1.2 |
Seifert-van Kampen Theorem
|
| Week 5 | Ch. 1.3 |
Classification of coverings, deck translations
|
| Week 6 | Ch. 4.1 |
Higher homotopy groups: definition, commutativity
|
| Week 7 | Ch. 4.1 |
CW complexes: Cellular approximations, CW homotopy groups
|
| Week 8 | Ch. 1.4 |
Fundamental groups of surfaces, classifying spaces
|
This syllabus leaves two extra weeks which should be distributed
as needed; later sections may be more than one week.