Graduate seminar in
SEIBERG-WITTEN THEORY AND TOPOLOGY OF 4-MANIFOLDS
Vector bundles. Connections and the curvature. Characteristic classes.
The universal bundle. Classification of connections. Hodge theory.
Spin geometry on 4-manifolds:
Spin groups and spin structures on a manifold. Almost complex and spin-C
structures. Clifford algebras. The spin connection. The Dirac operator.
The Atiyah-Singer index theorem.
The Seiberg-Witten theory:
The Seiberg-Witten equations. The moduli space and its compactness.
Transversality theorem. Topology of 4-manifolds. Seiberg-Witten
invariants. Dirac operators on Kahler manifolds. Invariants of Kahler
surfaces. The proof of Thom's conjecture.
Basic courses in differential geometry and topology.
Lectures on Seiberg-Witten invariants, by J. Moore;
The Seiberg-Witten equations and applications to the topology of
smooth four-manifolds, by J.Morgan