Spin^c-STRUCTURES AND SEIBERG-WITTEN EQUATIONS

The Seiberg-Witten equations, found at the end of the 20th century, are one of the main discoveries in the topology and geometry of four-dimensional Riemannian manifolds. They are defined in terms of a Spin(c)-structure that exists on any four-dimensional Riemannian manifold. Like the Yang-Mills equations, the Seiberg-Witten equations are the limit case of a more general supersymmetric Yang-Mills equations. However, unlike the conformally invariant Yang-Mills equations, the Seiberg-Witten equations are not scale invariant. Therefore, in order to obtain "useful information" from them, one must introduce a scale parameter lambda and pass to the limit as lambda -> 8. This is precisely the adiabatic limit studied in this paper.