Reading Group: Bott & Tu

Overview

This semester, I'd like to organize a reading group focusing on Bott and Tu's lovely book, Differential Forms in Algebraic Topology. The goal is to learn about cohomology from the point of view of differential geometry. My hope is to get to material on characteristic classes.

Talks

September 10 - Introduction and Preliminary Material - Brian Shin

Overview, category theory, linear algebra, and smooth manifolds


September 17 - The de Rham Complex and the Mayer-Vietoris Sequence - Brian Shin

§§1 and 2: Differential forms and de Rham cohomology (with and without compact support)


September 24 - Orientation, Integration, and Poincaré Lemmas - Brian Shin

§§3 and 4


October 1 - The Mayer-Vietoris Argument - Yigal Kamel

§5


October 8 - The Thom Isomorphism, pt. I - Zach Halladay

§6


October 15 - The Thom Isomorphism, pt. II- Zach Halladay

§6


October 22 - The General Mayer-Vietoris Principle, Examples, and Applications - Brian Shin

§§8 and 9


October 29 - Presheaves, Čech Cohomology, and Sphere Bundles - Johnson Tan

§10


November 5 - Chern Classes - ???

§20


November 12 - Splitting Principle - ???

§21


November 19 - Universal Complex Vector Bundle - ???

§23


November 26 - Fall Break

Extra credit reading assignment: §13 Monodromy


December 3 - ???- ???

§§21 and 23

Time and Place

We'll be meeting Thursdays from 2:00 to 3:00 p.m. Chicago Time. We'll be meeting via Zoom If you would like the coordinates for the meetings, please email me.