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

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.