Twistors, Self-Duality, and Spinᶜ Structures

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• Main Author: LeBrun, Claude
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211425
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Twistors, Self-Duality, and Spinᶜ Structures. Claude LeBrun. SIGMA 17 (2021), 102, 11 pages

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...