math 151c, spring 2023

This is the webpage for my spring 2023 section of Math 151c (algebraic and differential topology).

The syllabus is posted here. This is subject to minor revisions, as necessary. In the interest of transparency, all versions will remain available at this webpage.

schedule:

week topics readings homework due date

1 (4/3-4/7) smooth manifolds; vector bundles and operations thereamong §§1-3 hw1 4/12

2 (4/10-4/14) Stiefel--Whitney classes axiomatically §4 hw2 4/19

3 (4/17-4/21) Grassmann manifolds and Schubert cells §§5-6 hw3 4/26

4 (4/24-4/28) existence and uniqueness of Stiefel--Whitney classes §§7-8 hw4 5/3

5 (5/1-5/5) Euler classes; Thom isomorphism; computations for smooth manifolds §§9-11 hw5 5/10

6 (5/8-5/12) computations for smooth manifolds, cont. §11 hw6 5/17

7 (5/15-5/19) obstructions §12 hw7 5/24

8 (5/22-5/26) complex vector spaces and complex manifolds; Chern classes §§13-14 hw8 5/31

9 (5/31-6/2) Pontrjagin classes; Chern and Pontrjagin numbers §§15-16 hw9 6/7

week	topics	readings	homework	due date
1 (4/3-4/7)	smooth manifolds; vector bundles and operations thereamong	§§1-3	hw1	4/12
2 (4/10-4/14)	Stiefel--Whitney classes axiomatically	§4	hw2	4/19
3 (4/17-4/21)	Grassmann manifolds and Schubert cells	§§5-6	hw3	4/26
4 (4/24-4/28)	existence and uniqueness of Stiefel--Whitney classes	§§7-8	hw4	5/3
5 (5/1-5/5)	Euler classes; Thom isomorphism; computations for smooth manifolds	§§9-11	hw5	5/10
6 (5/8-5/12)	computations for smooth manifolds, cont.	§11	hw6	5/17
7 (5/15-5/19)	obstructions	§12	hw7	5/24
8 (5/22-5/26)	complex vector spaces and complex manifolds; Chern classes	§§13-14	hw8	5/31
9 (5/31-6/2)	Pontrjagin classes; Chern and Pontrjagin numbers	§§15-16	hw9	6/7