Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
MAT 215A: Topology
Approved: 2009-05-01, Dmitry Fuchs, Greg Kuperberg
Units/Lecture:
Fall, alternate years; 4 units; lecture/term paper or discussion section
Suggested Textbook: (actual textbook varies by instructor; check your
instructor)
Algebraic Topology, Allen Hatcher, Cambridge Univ, ($30), Dmitry Fuchs' handouts
Search by ISBN on Amazon: 0521795400
Search by ISBN on Amazon: 0521795400
Prerequisites:
Graduate standing or consent of instructor
Course Description:
Fundamental group and covering space theory. Homology and cohomology. Manifolds and duality. CW complexes. Fixed point theorems.
Suggested Schedule:
| 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 |
Additional Notes:
This syllabus leaves two extra weeks which should be distributed as needed; later sections may be more than one week.