Please log in to view module content:
Outline: The course will start with a refresher on smooth manifolds and their tangent bundles, before introducing more general vector bundles and fibre bundles.
It will then discuss in detail various aspects of calculus on manifolds, introducing the Lie derivative, the exterior derivative, connections, holonomy, curvature, and Stokes' Theorem.
This will be followed by an exposition of de Rham cohomology and its relation to singular and Cech cohomology.
Finally, the material will be brought together via an introduction to Chern-Weil theory and characteristic classes of vector bundles on manifolds.