Bott & Tu
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.
2020 September 10 - Introduction and Preliminary Material - Brian Shin
Overview, category theory, linear algebra, and smooth manifolds
2020 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)
2020 September 24 - Orientation, Integration, and Poincaré Lemmas - Brian Shin
§§3 and 4
2020 October 1 - The Mayer-Vietoris Argument - Yigal Kamel
2020 October 8 - The Thom Isomorphism, pt. I - Zach Halladay
2020 October 15 - The Thom Isomorphism, pt. II- Zach Halladay
2020 October 22 - The General Mayer-Vietoris Principle, Examples, and Applications - Brian Shin
§§8 and 9
2020 October 29 - Presheaves, Čech Cohomology, and Sphere Bundles - Johnson Tan
2020 November 5 - Chern Classes - ???
2020 November 12 - Splitting Principle - ???
2020 November 19 - Universal Complex Vector Bundle - ???
2020 November 26 - Fall Break
Extra credit reading assignment: §13 Monodromy
2020 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.