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Symmetry, Integrability and Geometry: Methods and Applications, 2021, Volume 17, 102, 11 pp.
DOI: https://doi.org/10.3842/SIGMA.2021.102 (Mi sigma1784) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Twistors, Self-Duality, and Spin${}^c$ Structures

Claude LeBrun

Department of Mathematics, Stony Brook University, Stony Brook, NY 11794-3651 USA
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DOI: https://doi.org/10.3842/SIGMA.2021.102
URL: https://www.imath.kiev.ua/~sigma/2021/102/
Abstract: The fact that every compact oriented 4-manifold admits spin$^c$ 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 spin$^c$ structures in any dimension.
Keywords: 4-manifold, spin$^c$ structure, twistor space, self-dual 2-form.
Funding agency Grant number
National Science Foundation DMS-1906267
This research was supported in part by NSF grant DMS-1906267.
Received: August 2, 2021; in final form November 15, 2021; Published online November 19, 2021
Bibliographic databases:
Document Type: Article
MSC: 53C27, 53C28, 57R15
Language: English
Citation: Claude LeBrun, “Twistors, Self-Duality, and Spin${}^c$ Structures”, SIGMA, 17 (2021), 102, 11 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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