Twistors, Self-Duality, and Spinc Structures

Claude Lebrun

doi:10.3842/SIGMA.2021.102

Twistors, Self-Duality, and Spin^c Structures

Claude Lebrun

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English
Article number	102
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	17
DOIs	https://doi.org/10.3842/SIGMA.2021.102
State	Published - 2021

Keywords

4-manifold
Self-dual 2-form
Spin structure
Twistor space

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10.3842/SIGMA.2021.102

Cite this

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abstract = "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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AB - 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.

KW - 4-manifold

KW - Self-dual 2-form

KW - Spin structure

KW - Twistor space

UR - https://www.scopus.com/pages/publications/85122299091

U2 - 10.3842/SIGMA.2021.102

DO - 10.3842/SIGMA.2021.102

M3 - Article

AN - SCOPUS:85122299091

SN - 1815-0659

VL - 17

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

M1 - 102

ER -

Twistors, Self-Duality, and Spin^c Structures

Abstract

Keywords

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