This is a continuation of the course 532: Introduction to Differential Geometry. However it differs from 533 in previous semesters. Depending on time and progress, topics may include:
1. Review connections and curvatures on vector bundles.
2. Connections on principal bundles.
3. Harmonic forms and Hodge Theorem.
4. Chern classes.
5. Basic gauge theory.
References:
Kobayashi-Nozimu: Foundations of Differential Geometry
Jost: Riemannian Geometry and Geometric Analysis
Warner: Foundations of Differentiable Manifolds and Lie Groups
Kobayashi-Nozimu: Foundations of Differential Geometry
532