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Instantons on Hopf surfaces and monopoles on solid tori.

A simple example of a Hopf surface 3C is the complex surface C\{0} modulo the action of an infinite cyclic group of dilations of C. The surface 3tf carries a natural conformal structure, so one can consider (SU (2)) instantons [AHS] on it. The Solutions to the anti-self-duality equations (instantons) are parameterized by points in a finite dimensional manifold, the instanton moduli space. Recently, Buchdahl [B] proved that on a complex surface (not necessarily Kahler) one can obtain such moduli spaces äs moduli of stable holomorphic bundles on the surface. Our first goal is to exploit this theorem to give a description of instanton moduli on the Hopf surface. Specific examples of such instantons can be found in [Br 1].