This course is a first course in algebraic topology. The emphasis is on homology and cohomology theory, including cup products, Kunneth formulas, and (possibly) cohomology operations.

The course syllabus can be found here. (PDF format)

The course textbook is Algebraic topology, by Allen Hatcher. This text is freely available online, or can be purchased through the bookstore.

Further suggested reading:

• An introduction to algebraic topology, by Joseph J. Rotman.
• A basic course in algebraic topology, by William S. Massey.
• Topology and geometry, by Glen E. Bredon.
• Differential forms in algebraic topology, by Bott and Tu, which is not directly related to the course material but a very good discussion of related material.
• Algebraic topology, by Edwin H. Spanier, which is a good reference but not recommended for a first attempt.

Assignments

There will be weekly problem sets posted here. The course has no final exam.

Problem set 1. (Due September 13.) (Updated Sept. 8)

Problem set 2. (Due September 20.) (Updated Sept. 19 to change an n to an n+1.)

Problem set 3. (Due September 27.)

Problem set 4. (Due October 4.)

Problem set 5. (Due October 11.)

Problem set 6. (Due October 18.) (Updated Oct. 11 because I wrote page 367 instead of 267, and Oct. 13 to change problem 3.)

Problem set 7. (NOTE! Now due Friday, October 27.) (Updated Oct. 21 to fix a couple of typos in problem 5.)

Problem set 8. (Due November 1.)

Problem set 9. (Due November 8.) (Updated Oct. 31 to fix a sign.)

Problem set 10. (Due FRIDAY, November 17.)

Problem set 11. (Due December 1.) (Updated Nov. 19 to change (X x X) to X in problem 4.)

Problem set 12. (Final assignment. Due December 8.)

Contact information

I can be contacted as follows.

• By email: tlawson (at) math.mit.edu
• By phone: 3-4385
• By foot: Room 2-171