Index Theorem and Characteristic Classes

Lecture 1. Vector Bundles

Lecture 2. Projective Spaces, Grassmannians, and Pullbacks

Lecture 3. Connections Vector Bundles. Curvature

Lecture 4. More on Connections on Vector Bundles. Principal Bundle

Lecture 5. The Chern–Weil Theory

Lecture 6. Complex Vector Bundle. Chern Classes

Lecture 7. Real Vector Bundles

Lecture 8. Partial Derivative Operators

Lecture 9. The Symbol of a Differential Operator

Lecture 10. Atiyah–Singer Index Theorem for Dirac-Type Operators. Clifford Algebra

Lecture 11. Spinor Representation

Lecture 12. Geometric Dirac Operator