Math 225A Class Schedule

Math 225A: Differential Topology

Class Schedule

The topics are tentative but the due dates are not.

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!

Last modified: November 23, 2015.