Fibre bundles and connections, Spring 2012
Instructors: Norbert Poncin and Vladimir Dotsenko
The objective of this course is to give students an overview of the theory of fibre bundles, vector bundles
and principal bundles, and of connections on vector and principal bundles. Each lecture will contain intuitive material, definitions, propositions and theorems (with complete proofs for the most instructional ones), as well as
exercises and explanations of links with physics.
- Lie groups and Lie algebras.
- Fibre and vector bundles.
- Connections on vector bundles, covariant derivative, parallel transport, curvature, torsion, Levi-Civita connection, holonomy.
- Principal bundles, associated and reduced bundles.
- Connections on principal bundles, connection 1-form, covariant derivative,
curvature, holonomy, gauge theory.
- Characteristic classes, Chern-Weil theory.