Publisher's Synopsis
The field of Seiberg-Witten gauge theory has become a well-established part of the differential topology of four-manifolds and three-manifolds. This title offers an introduction and a review of the state of research. The first part of the book gives an introduction of Seiberg-Witten theory of four-dimensional manifolds. In the second part, the author introduces the dimensional reduction and uses it to describe Seiberg-Witten in three-dimensional manifolds. In both parts, the Seiberg-Witten equations are derived, the moduli spaces of solutions are constructed, and the corresponding invariants of manifolds are introduced. In the third part, the author gives an overview of geometric and topological results obtained via Seiberg-Witten theory. Through all these parts of the book, Seiberg-Witten gauge theory is considered as a completely self-contained subject and no a priori knowledge of Donaldson theory is assumed.
