We will be using Algebraic Topology from a Homotopical Viewpoint by Aguilar, Gitler, and Prieto. Here is the tentative outline:
- (Week 1) “Basic concepts and notation.” This includes a few facts about smooth maps, in particular Sard’s lemma, which you can find a proof of in Chapter 3 of Milnor’s short book. There are no exercises for the first meeting.
- (Week 2) Chapter 1, Exercise 1.3.10, Sections 2.1 + 2.2, Exercise 2.2.2 + 2.2.3.
- (Week 3) Sections 2.3 + 2.4, Exercise 2.4.14 + 2.4.33 + 2.4.39.
- (Week 4) Section 2.5 – 2.10, Exercise 2.5.19 + 2.6.16 + 2.6.18 + 2.7.8 + 2.9.9 + 2.10.11.
- (Week 5) Sections 3.1 + 3.2, Exercise 3.1.3 + 3.2.3 + 3.2.14 (b).
- (Week 6) Sections 3.3 – 3.5, Exercise 3.3.6 + 3.3.21 + 3.4.9.
- (Week 7) Sections 4.1 – 4.4, Exercise 4.1.15 + 4.2.6 + 4.2.17 + 4.3.6 + 4.3.15.
- (Week 8) Sections 4.5 + 4.6, Exercise 4.5.16 + 4.5.17 + 4.5.30 + 4.6.11.
- (Week 9) Section 5.1, Exercise 5.1.4 + 5.1.16 + 5.1.18 + 5.1.39.
- (Week 10) Sections 5.2 + 5.3. Exercise 5.2.6 + 5.3.22 + 5.3.27.
- (Week 11) Sections 6.1 + 7.1. Exercise 7.1.14 + 7.1.32
- (Week 12) Sections 7.2 + 7.3 + 7.4. Exercise 7.3.16.
- (Week 13) Chapter 8 (skip the details to get the big picture).
- (Week 14) Chapter 9 (“).
- (Week 15) Presentations.