*
Graduate seminar in
*

SEIBERG-WITTEN THEORY AND TOPOLOGY OF 4-MANIFOLDS

*
Seminar outline: *

## Preliminaries:

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.
# Prerequisites:

## Basic courses in differential geometry and topology.

# Books:

*Lectures on Seiberg-Witten invariants,* by J. Moore;

*The Seiberg-Witten equations and applications to the topology of
smooth four-manifolds,* by J.Morgan