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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210602 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the Relationship between Classical and Deformed Hopf Fibrations. Tomasz Brzeziński, James Gaunt and Alexander Schenkel. SIGMA 16 (2020), 008, 29 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862632198410076160 |
|---|---|
| author | Brzeziński, Tomasz Gaunt, James Schenkel, Alexander |
| author_facet | Brzeziński, Tomasz Gaunt, James Schenkel, Alexander |
| citation_txt | On the Relationship between Classical and Deformed Hopf Fibrations. Tomasz Brzeziński, James Gaunt and Alexander Schenkel. SIGMA 16 (2020), 008, 29 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-17T12:04:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210602 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:04:19Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Brzeziński, Tomasz Gaunt, James Schenkel, Alexander 2025-12-12T10:38:24Z 2020 On the Relationship between Classical and Deformed Hopf Fibrations. Tomasz Brzeziński, James Gaunt and Alexander Schenkel. SIGMA 16 (2020), 008, 29 pages 1815-0659 2020 Mathematics Subject Classification: 81T75; 16T05 arXiv:1811.10913 https://nasplib.isofts.kiev.ua/handle/123456789/210602 https://doi.org/10.3842/SIGMA.2020.008 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. We would like to thank Christian Lomp and Alexander Vishik for their useful comments related to this work. We would also like to thank the anonymous referees for their valuable comments and suggestions that helped us to improve this manuscript. The research of T.B. was partially supported by the Polish National Science Centre grant 2016/21/B/ST1/02438. A.S. gratefully acknowledges the financial support of the Royal Society (UK) through a Royal Society University Research Fellowship, a Research Grant, and an Enhancement Award. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Relationship between Classical and Deformed Hopf Fibrations Article published earlier |
| spellingShingle | On the Relationship between Classical and Deformed Hopf Fibrations Brzeziński, Tomasz Gaunt, James Schenkel, Alexander |
| title | On the Relationship between Classical and Deformed Hopf Fibrations |
| title_full | On the Relationship between Classical and Deformed Hopf Fibrations |
| title_fullStr | On the Relationship between Classical and Deformed Hopf Fibrations |
| title_full_unstemmed | On the Relationship between Classical and Deformed Hopf Fibrations |
| title_short | On the Relationship between Classical and Deformed Hopf Fibrations |
| title_sort | on the relationship between classical and deformed hopf fibrations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210602 |
| work_keys_str_mv | AT brzezinskitomasz ontherelationshipbetweenclassicalanddeformedhopffibrations AT gauntjames ontherelationshipbetweenclassicalanddeformedhopffibrations AT schenkelalexander ontherelationshipbetweenclassicalanddeformedhopffibrations |