On the Relationship between Classical and Deformed Hopf Fibrations

The θ-deformed Hopf fibration S³θ → S² over the commutative 2-sphere is compared with its classical counterpart. It is shown that there exists a natural isomorphism between the corresponding associated module functors and that the affine spaces of classical and deformed connections are isomorphic. T...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2020
Main Authors: Brzeziński, Tomasz, Gaunt, James, Schenkel, Alexander
Format: Article
Language:English
Published: Інститут математики НАН України 2020
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/210602
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:On the Relationship between Classical and Deformed Hopf Fibrations. Tomasz Brzeziński, James Gaunt and Alexander Schenkel. SIGMA 16 (2020), 008, 29 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary:The θ-deformed Hopf fibration S³θ → S² over the commutative 2-sphere is compared with its classical counterpart. It is shown that there exists a natural isomorphism between the corresponding associated module functors and that the affine spaces of classical and deformed connections are isomorphic. The latter isomorphism is equivariant under an appropriate notion of infinitesimal gauge transformations in these contexts. Gauge transformations and connections on associated modules are studied and are shown to be sensitive to the deformation parameter. A homotopy theoretic explanation for the existence of a close relationship between the classical and deformed Hopf fibrations is proposed.
ISSN:1815-0659