G-invariant spin structures on spheres

Daura Serrano, Jordi; Kohn, Michael; Lawn, Marie-Amélie

Abstract

We examine which of the compact connected Lie groups that act transitively on spheres of different dimensions leave the unique spin structure of the sphere invariant. We study the notion of invariance of a spin structure and prove this classification in two different ways; through examining the differential of the actions and through representation theory.

Citation

Daura Serrano, J., Kohn, M., & Lawn, M. (2022). G-invariant spin structures on spheres. Annals of Global Analysis and Geometry, 62(2), 437-455. https://doi.org/10.1007/s10455-022-09855-z

• Journal Article Type: Article
• Acceptance Date: May 24, 2022
• Online Publication Date: Jun 30, 2022
• Publication Date: 2022-09
• Deposit Date: Nov 18, 2022
• Journal: Annals of Global Analysis and Geometry
• Print ISSN: 0232-704X
• Electronic ISSN: 1572-9060
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 62
• Issue: 2
• Pages: 437-455
• DOI: https://doi.org/10.1007/s10455-022-09855-z
• Public URL: https://durham-repository.worktribe.com/output/1185823
• Related Public URLs: https://arxiv.org/abs/2109.09580