INTRODUCTION

The purpose of this article is to give a classification of invariant SU(2)-instantons on S4 for some equivariant SU(2)-bundles over S4 and to give some applications. We use the term instanton for anti-self-dual connection here. It is well known that the moduli spaces of SU(2)-instantons on the standard four sphere S4 are smooth manifolds. When a group Г acts on S4 isometrically and P is a Г-invariant SU(2)- bundle, the moduli space M(P) of Г-invariant instantons on P is defined as the quotient of the space of Г-invariant instantons divided by the Г-equivariant gauge transformations. Then M(P) has a natural smooth structure as well. Instantons on S4 are classified by the ADHM-construction [2] or the monad description [5], so, in principle, we have a description of invariant instantons. On the other hand, for some group actions the invariant instantons have some geometric interpretation: M. F. Atiyah pointed out as an important example that when Г is the rotations around S2 in S4, the Г-invariant instantons are interpreted as hyperbolic monopoles [1]. In this article we consider subgroups of the maximal torus of SO(4) as F and Г-equivariant SU(2)-bundles over S4 for which the moduli spaces of invariant instantons are one-dimensional, in particular when Г is a finite cyclic group Za of order a.