STRONG CONNECTIONS ON QUANTUM PRINCIPAL BUNDLES

A gauge invariant notion of a strong connection is presented and chara cterized. It is then used to justify the way in which a global curvatu re form is defined. Strong connections are interpreted as those that a re induced from the base space of a quantum bundle. Examples of both s trong and non-strong connections are provided. In particular, such con nections are constructed on a quantum deformation of the two-sphere fi bration S-2 --> RP(2). A certain class of strong U-q(2)-connections on a trivial quantum principal bundle is shown to be equivalent to the c lass of connections on a free module that are compatible with the q-de pendent hermitian metric. A particular form of the Yang-Mills action o n a trivial U-q(2)-bundle is investigated. It is proved to coincide wi th the Yang-Mills action constructed by A. Connes and M. Rieffel. Furt hermore, it is shown that the moduli space of critical points of this action functional is independent of q.