Nontrivial Deformation of a Trivial Bundle

Abstract

The $\mathrm{SU}(2)$-prolongation of the Hopf fibration $S^3\to S^2$ is a trivializable principal $\mathrm{SU}(2)$-bundle. We present a noncommutative deformation of this bundle to a quantum principal ${\mathrm{SU}}_q(2)$-bundle that is not trivializable. On the other hand, we show that the ${\mathrm{SU}}_q(2)$-bundle is piecewise trivializable with respect to the closed covering of $S^2$ by two hemispheres intersecting at the equator.

The present paper has been extracted from an earlier version of arXiv:1101.0201, so that there are some overlaps in introductory parts and standard definitions

References in corpus (4)

• Noncommutative Geometry Approach to Principal and Associated Bundles
• Free actions of compact quantum group on unital C*-algebras
• Piecewise principal comodule algebras
• Local Proof of Algebraic Characterization of Free Actions