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arXiv · 1310.7664

Nontrivial Deformation of a Trivial Bundle

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.

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Piotr M. Hajac, Bartosz Zieliński. 2013-10-29. Nontrivial Deformation of a Trivial Bundle. https://doi.org/10.3842/sigma.2014.031

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