Nontrivial Deformation of a Trivial Bundle

Abstract

The SU(2)-prolongation of the Hopf fibration S³→S² is a trivializable principal SU(2)-bundle. We present a noncommutative deformation of this bundle to a quantum principal SUq(2)-bundle that is not trivializable. On the other hand, we show that the SUq(2)-bundle is piecewise trivializable with respect to the closed covering of S² by two hemispheres intersecting at the equator.