Course Syllabus

The topics of every lecture appear here, possibly tentatively. Chapter references refer to the course notes.

Sep 4 Introduction to vector bundles. Definition as spaces over a base space and as sheaved Chapter 1–2.2
Sep 12 Fiber bundles and cocycles; operations on bundles Chapter 2.3-2.5
Sep 19 smooth manifolds, tangent bundles, and bundles with additional structure. Stiefel and Grassmann manifolds und universal bundles Chapter 2.6, 3.2
Sep 26 simplicial spaces and geometric realization Chapter 3.3
Oct 3 Paracompactness, classifying spaces Chapter 3.5-3.6
Oct 10 Čech cohomology I Chapter 4.1-4.2
Oct 17 Čech cohomology II Chapter 4.3-4.7

 

 

Course Summary:

Date Details Due