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arXiv · 2108.01739

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

Claude LeBrun
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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.

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Claude LeBrun. 2021-08-03. Twistors, Self-Duality, and Spin$^c$ Structures. https://doi.org/10.3842/sigma.2021.102

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