Twistors, Self-Duality, and Spin$^c$ Structures
Differential Geometry
2021-11-22 v3 Geometric Topology
Abstract
The fact that every compact oriented 4-manifold admits spin 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 structures in any dimension.
Keywords
Cite
@article{arxiv.2108.01739,
title = {Twistors, Self-Duality, and Spin$^c$ Structures},
author = {Claude LeBrun},
journal= {arXiv preprint arXiv:2108.01739},
year = {2021}
}