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On the Relationship between Classical and Deformed Hopf Fibrations

Tomasz Brzezinski Orcid Logo, James Gaunt, Alexander Schenkel

Symmetry, Integrability and Geometry: Methods and Applications, Volume: 16, Issue: 008

Swansea University Author: Tomasz Brzezinski Orcid Logo

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DOI (Published version): 10.3842/sigma.2020.008

Abstract

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
ISSN: 1815-0659
Published: SIGMA (Symmetry, Integrability and Geometry: Methods and Application) 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa53623
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Abstract: 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.
Keywords: noncommutative geometry; principal comodule algebras; noncommutative principal bundles; Hopf fibrations; homotopy equivalence
College: Faculty of Science and Engineering
Issue: 008

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