Nontrivial Deformation of a Trivial Bundle

Piotr M. Hajac; Bartosz Zieliński

doi:10.3842/SIGMA.2014.031

Nontrivial Deformation of a Trivial Bundle

Quantum Algebra 2014-03-31 v2

Authors: Piotr M. Hajac , Bartosz Zieliński

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Abstract

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

Keywords

Hopf fibration principal bundle noncommutative deformation quantum group SU_q(2) trivializable piecewise trivializable

Cite

@article{arxiv.1310.7664,
  title  = {Nontrivial Deformation of a Trivial Bundle},
  author = {Piotr M. Hajac and Bartosz Zieliński},
  journal= {arXiv preprint arXiv:1310.7664},
  year   = {2014}
}

Comments

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

Nontrivial Deformation of a Trivial Bundle

Abstract

Keywords

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