Classifying spaces for quantum principal bundles

Abstract

A construction of a quantum analogue of principal bundles is discussed. Deformations of quantum groups in the sense of Woronowicz allow to relax the condition of local triviality of a principal bundle; the fibres need not be all identical any longer. This leads to deformations of structure group and bundles. There is still a classifying space in the sense that homotopy classes of bundles are classified by homotopy classes of maps from the base space into the classifying space.