Math 225A: Differential Topology
|
Date | Tentative topic |
Homework
|
9/25 |
Review of topology and linear algebra |
HW1,
due 10/2 |
9/28 |
Review of differentiation |
|
9/30 |
Manifolds; examples |
|
10/2 |
Smooth functions and smooth maps |
HW2,
due 10/9 |
10/5 |
The inverse function theorem |
|
10/7 |
Submersions |
|
10/9 |
Immersions and embeddings | HW3,
due 10/16 |
10/12 |
Tangent spaces, Day I | |
10/14 |
Tangent spaces, Day II | |
10/16 |
The tangent bundle | HW4,
due 10/23 |
10/19 |
Cotangent bundles and 1-forms | |
10/21 |
Lie groups | |
10/23 |
Vector bundles, Day I | HW5,
due 10/30 |
10/26 |
Vector bundles, Day II; partition of unity | |
10/28 |
Vector fields | |
10/30 |
Sard's theorem | HW6,
due 11/6 |
11/2 |
Transversality, Day I | |
11/4 |
Transversality, Day II | |
11/6 |
Morse functions | HW7,
due 11/13 |
11/9 |
Whitney embedding theorem | |
11/11 |
No class (Veterans Day) |
|
11/13 |
Orientations | HW8,
due 11/20 |
11/16 |
Oriented intersection numbers | |
11/18 |
Degree |
|
11/20 |
Applications of degree; winding numbers | HW9, due 12/4 |
11/23 |
More intersection
theory; Euler characteristic |
|
11/25 |
Lefschetz fixed point theorem | |
11/27 |
No class (Thanksgiving break) |
|
11/30 |
Lefschetz fixed point theorem, Day II | |
12/1 (Tues) |
Poincaré-Hopf theorem
(lecture given during discussion: 12pm, MS 6221) |
|
12/2 |
Hopf degree theorem
(last day of class) |
|
12/4 |
No class (but
discussion held during class hour: 12pm, MS
5137) |
|
Final exam
is take-home! |