Reading course on characteristic classes

This is an informal reading course on characteristic classes following the book of Milnor and Stasheff [MS].
We will be meeting on Tuesdays at 11am in 3106.

Prerequisites: MAT 239 and MAT 215AB are very strict prerequisites. You have to have very good working knowledge of smooth manifolds and transversality, homotopy equivalence and homology. If you have not taken these classes yet, you need to take them first. Some algebraic geometry, differential geometry or symmetric functions might be helpful, but not required.


9/26 (Eugene) Introduction to vector bundles (MS, Sections 2-3) notes , HW 1


10/10 (Eugene) Overview of cohomology (Hatcher, Section 3) notes

10/17 (Melissa) Stiefel-Whitney classes (MS, Section 4) notes , more notes

10/24 (Eugene) Section 4 continued notes , HW 2

10/31 (Yuze) Grassmann manifolds and universal bundles (MS, Section 5) notes

11/7 (Eugene) Cell structure for Grassmann manifolds (MS, Section 6) notes

11/14 (Eugene) Cohomology ring for infinite Grassmann manifolds (MS, Section 7) notes

11/21 Oriented bundles and the Euler class; Computations for smooth manifolds (MS, Sections 9 and 11) notes

11/28 TBD

12/5 (Jon) Complex vector bundles and complex manifolds; Chern Classes (MS, Sections 13-14)