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This is the webpage for my spring 2022 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 (3/28-4/1) smooth manifolds, vector bundles §§1-2 hw1 4/6
2 (4/4-4/8) operations on vector bundles, Stiefel--Whitney classes axiomatically §§3-4 hw2 4/13
3 (4/11-4/15) Grassmann manifolds and Schubert decompositions §§5-7 hw3 4/20
4 (4/18-4/22) existence and uniqueness of Stiefel--Whitney classes; Euler classes §§7-9 hw4 4/27
5 (4/25-4/29) Thom isomorphism; computations for smooth manifolds §§10-11 hw5 5/4
6 (5/2-5/6) computations cont.; obstructions §§11-12 hw6 5/11
7 (5/9-5/13) obstructions cont.; complex vector bundles and complex manifolds; Chern classes §§12-14 hw7 5/18
8 (5/16-5/20) Chern classes, cont.; Pontrjagin classes §§14-15 hw8 5/25
9 (5/23-5/27) Chern and Pontrjagin numbers §16 hw9 7/1