Math 225C: Algebraic Topology
|
| Date | Tentative topic |
Homework
|
| 4/1 (Mon) |
Homotopy and composition of paths |
HW1,
due 4/8 |
| 4/3 (Wed) |
Fundamental groups, Day I |
|
| 4/5 (Fri) |
Fundamental groups, Day II (homotopy invariance) |
|
| 4/8 |
Covering spaces; homotopy lifting property | HW2,
due 4/15 |
| 4/10 |
Computation of \pi_1(S^1) and \pi_1(S^n) | |
| 4/12 |
Seifert-van Kampen theorem, Day I |
|
| 4/15 |
Seifert-van Kampen theorem, Day II | HW3,
due 4/22 |
| 4/17 |
Computations of \pi_1 and definition of universal cover |
|
| 4/19 |
Lifting properties of covering
spaces |
|
| 4/22 |
Construction of the universal cover |
HW4,
due 4/29 |
| 4/24 |
Classification of covering spaces | |
| 4/26 |
Normal covers | |
| 4/29 |
\Delta-complexes | HW5,
due 5/6 |
| 5/1 |
Simplicial homology | |
| 5/3 |
Singular homology | |
| 5/6 |
Functoriality and homotopy invariance | HW6,
due 5/13 |
| 5/8 |
Exact sequences; Mayer-Vietoris sequence | |
| 5/10 |
More on Mayer-Vietoris; Barycentric subdivision | |
| 5/13 |
More on barycentric subdivision | HW7,
due 5/20 |
| 5/15 |
Relative homology | |
| 5/17 |
Excision | |
| 5/20 |
Homology and the fundamental group | HW8,
due 5/29 |
| 5/22 |
Equivalence of simplicial and singular homology; homology axioms | |
| 5/24 |
Degree | |
| 5/27 |
University Holiday (Memorial Day) | HW9, due 6/3 |
| 5/29 |
Cellular homology | |
| 5/31 |
Cellular homology computations | |
| 6/3 |
Cohomology, Day I | |
| 6/5 |
Cohomology, Day II | |
| 6/7 |
Cohomology, Day III | |
| Final exam is
take-home! |