Math 225C: Algebraic Topology
|
| Date | Tentative topic |
Homework
|
| 3/28 (Mon) |
Homotopy and composition of paths |
HW1,
due 4/4 |
| 3/30 (Wed) |
Fundamental groups, Day I |
|
| 4/1 (Fri) |
Fundamental groups, Day II (homotopy invariance) |
|
| 4/4 |
Covering spaces; homotopy lifting property | HW2,
due 4/11 |
| 4/6 |
Computation of \pi_1(S^1) and \pi_1(S^n) | |
| 4/8 |
Seifert-van Kampen theorem, Day I |
|
| 4/11 |
Seifert-van Kampen theorem, Day II | HW3,
due 4/18 |
| 4/13 |
Computations of \pi_1; universal cover |
|
| 4/15 |
Universal cover; lifting properties |
|
| 4/18 |
Classification of covering spaces |
HW4,
due 4/25 |
| 4/20 |
Normal covers |
|
| 4/22 |
\Delta-complexes | |
| 4/25 |
Simplicial homology | HW5,
due 5/2 |
| 4/27 |
Singular homology | |
| 4/29 |
Functoriality and homotopy invariance | |
| 5/2 |
Exact sequences; Mayer-Vietoris
sequence |
HW6,
due 5/9 |
| 5/4 |
More on Mayer-Vietoris; Barycentric
subdivision |
|
| 5/6 |
More on barycentric
subdivision |
|
| 5/9 |
Relative homology |
HW7,
due 5/16 |
| 5/11 |
Excision |
|
| 5/13 |
Homology and the
fundamental group |
|
| 5/16 |
Equivalence of simplicial and singular homology;
homology axioms |
HW8,
due 5/23 |
| 5/18 |
Degree |
|
| 5/20 |
Cellular homology | |
| 5/23 |
Cellular homology computations | HW9, due 6/3(revised version) |
| 5/25 |
Cohomology, Day I |
|
| 5/27 |
Cohomology, Day II |
|
| 5/30 |
University Holiday
(Memorial Day) |
|
| 6/1 |
Cohomology, Day III |
|
| 6/3 |
Cup products |
|
| Final exam
is take-home! |