Differentialgeometrie III/Differential Geometry III

* Bundles, connections, covariant derivatives, curvature

* Characteristic classes

* Dirac operators, Laplacians

* Sobolev spaces of sections

* Harmonic forms and Hodge decomposition

* Fredholm theory, index theorems   (without proof)

* Complex bundles over Riemann surfaces, Riemann Roch theorem

* Pseudo-holomorphic curves and symplectic geometry

Possible topics if time permits: Anti-selfdual connections and Donaldson theory, Seiberg-Witten equations