Part 3: Fiber Bundles
Fiber Bundles
Principal bundles, associated bundles, frame bundle, and bundle classification
Gauge Connections
Connection 1-forms, curvature 2-forms, gauge transformations, and Yang-Mills equations
Characteristic Classes
Chern classes, Pontryagin classes, Euler class, and the splitting principle
Chern Weil
Chern-Weil homomorphism, invariant polynomials, Chern-Simons forms, and transgression