G-invariant Spin Structures on Spheres

20 Sep 2021 · Jordi Daura Serrano, Michael Kohn, Marie-Amélie Lawn ·

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.