G-invariant Spin Structures on Spheres

Published 20 Sep 2021 in math.DG | (2109.09580v2)

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.

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