On the Relationship between Classical and Deformed Hopf Fibrations

Tomasz Brzeziński, James Gaunt, Alexander Schenkel

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.
Original languageEnglish
JournalSymmetry, Integrability and Geometry: Methods and Applications
Issue number8
Publication statusPublished - 23 Feb 2020


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