On the relationship between classical and deformed Hopf fibrations

Brzezi?ski, Tomasz; Gaunt, James; Schenkel, Alexander

Abstract

The ?-deformed Hopf fibration S3??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.

Citation

Brzezi?ski, T., Gaunt, J., & Schenkel, A. (2020). On the relationship between classical and deformed Hopf fibrations. Symmetry, Integrability and Geometry: Methods and Applications, 16, https://doi.org/10.3842/sigma.2020.008

• Journal Article Type: Article
• Acceptance Date: Feb 17, 2020
• Online Publication Date: Feb 23, 2020
• Publication Date: 2020
• Deposit Date: Mar 4, 2020
• Publicly Available Date: Mar 4, 2020
• Journal: Symmetry, Integrability and Geometry: Methods and Applications
• Peer Reviewed: Peer Reviewed
• Volume: 16
• Article Number: 008
• DOI: https://doi.org/10.3842/sigma.2020.008
• Keywords: noncommutative geometry; principal comodule algebras; noncommutative principal bundles; Hopf fibrations; homotopy equivalence.
• Public URL: https://nottingham-repository.worktribe.com/output/2460441
• Publisher URL: https://www.emis.de/journals/SIGMA/2020/008/