Twistors, Self-Duality, and Spinᶜ Structures
The fact that every compact oriented 4-manifold admits spinᶜ structures was proved long ago by Hirzebruch and Hopf. However, the usual proof is neither direct nor transparent. This article gives a new proof using twistor spaces that is simpler and more geometric. After using these ideas to clarify v...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2021 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211425 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Twistors, Self-Duality, and Spinᶜ Structures. Claude LeBrun. SIGMA 17 (2021), 102, 11 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862620909050789888 |
|---|---|
| author | LeBrun, Claude |
| author_facet | LeBrun, Claude |
| citation_txt | Twistors, Self-Duality, and Spinᶜ Structures. Claude LeBrun. SIGMA 17 (2021), 102, 11 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The fact that every compact oriented 4-manifold admits spinᶜ structures was proved long ago by Hirzebruch and Hopf. However, the usual proof is neither direct nor transparent. This article gives a new proof using twistor spaces that is simpler and more geometric. After using these ideas to clarify various aspects of four-dimensional geometry, we then explain how related ideas can be used to understand both spin and spinᶜ structures in any dimension.
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| first_indexed | 2026-03-14T12:56:54Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211425 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T12:56:54Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | LeBrun, Claude 2026-01-02T08:30:16Z 2021 Twistors, Self-Duality, and Spinᶜ Structures. Claude LeBrun. SIGMA 17 (2021), 102, 11 pages 1815-0659 2020 Mathematics Subject Classification: 53C27; 53C28; 57R15 arXiv:2108.01739 https://nasplib.isofts.kiev.ua/handle/123456789/211425 https://doi.org/10.3842/SIGMA.2021.102 The fact that every compact oriented 4-manifold admits spinᶜ structures was proved long ago by Hirzebruch and Hopf. However, the usual proof is neither direct nor transparent. This article gives a new proof using twistor spaces that is simpler and more geometric. After using these ideas to clarify various aspects of four-dimensional geometry, we then explain how related ideas can be used to understand both spin and spinᶜ structures in any dimension. This article is dedicated to my friend and teacher, Sir Roger Penrose, in celebration of his ninetieth birthday and recent Nobel Prize in Physics. It is a pleasure to thank Dennis Sullivan for his advice and encouragement, and Jiahao Hu for some very illuminating conversations. This research was supported in part by NSF grant DMS-1906267. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Twistors, Self-Duality, and Spinᶜ Structures Article published earlier |
| spellingShingle | Twistors, Self-Duality, and Spinᶜ Structures LeBrun, Claude |
| title | Twistors, Self-Duality, and Spinᶜ Structures |
| title_full | Twistors, Self-Duality, and Spinᶜ Structures |
| title_fullStr | Twistors, Self-Duality, and Spinᶜ Structures |
| title_full_unstemmed | Twistors, Self-Duality, and Spinᶜ Structures |
| title_short | Twistors, Self-Duality, and Spinᶜ Structures |
| title_sort | twistors, self-duality, and spinᶜ structures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211425 |
| work_keys_str_mv | AT lebrunclaude twistorsselfdualityandspincstructures |