wk |
date |
reading assignment |
topic |
1 |
3/27 |
Ch 0, p. 5-10 |
CW complexes; operations on spaces |
|
3/29 |
Ch 0, p. 1-4, 11-13 |
Homotopy equivalence |
|
3/31 |
Ch 0, p. 14-16 |
Homotopy Extension Property |
| | Problem set #1 | | |
2 |
4/3 |
Ch 1.1, p. 21-24, 29-33 |
Winding Number |
|
4/5 |
Ch 1.1, p. 25-28 |
Fundamental group |
|
4/7 |
Ch 1.1, p. 34-37 |
Functoriality |
| | Problem set #2 | | |
3 |
4/10 |
Ch 1.2, p. 40-42, 44 |
Van Kampen, surjectivity |
|
4/12 |
Ch 1.2, p. 43-46 |
Van Kampen, kernel |
|
4/14 |
Ch 1.2, p. 46-52 |
Van Kampen, CW complexes |
| | Homework from Hatcher: | p. 53-54: Problems 4, 9, 8, 10, 14, 16. | |
4 |
4/17 |
|
(no class) |
|
4/19 |
Ch 1.3, p. 56-63 |
Lifting properties |
|
4/21 |
- |
(continued) |
5 |
4/24 |
Ch 1.3, p. 63-65 |
Universal cover |
|
4/26 |
Ch 1.3, p. 66-68 |
Galois correspondence |
|
4/28 |
Ch 1.3, p. 70-74 |
Deck transformations |
| | Problem set #4 | | |
6 |
5/1 |
Ch 2, 2.1, p. 95-107 |
Simplicial homology |
|
5/3 |
Ch 2.1, p. 108-110 |
Singular homology |
|
5/5 |
Ch 2.1, p. 111-113 |
Homotopy invariance |
| | Problem set #5 | | |
7 |
5/8 |
Ch 2.1, p. 113-118 |
Long exact sequence |
|
5/10 |
Ch 2.1, p. 119-126 |
Excision |
|
5/12 |
Ch 2.1, p. 127-130 |
Eilenberg-Steenrod axioms |
|
|
Ch 2.3, p. 160-165 |
|
| | Homework from Hatcher: | p. 132-133: Problems 16, 18, 20, 21, 24; p. 165 Problem 4. | |
8 |
5/15 |
Ch 2.2, p. 134-140 |
Cellular homology |
|
5/17 |
Ch 2.2, p. 141-148 |
Computations |
|
5/19 |
Ch 2.1, p. 149-153 |
Mayer-Vietoris |
| | Problem set #7 | | |