2019/02/17 by Yalcinkaya, Eyup
#FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1902.06293
In this paper, we introduce the classification of equivariant principal bundles over the 2-sphere. Isotropy representations provide tools for understanding the classification of equivariant principal bundles. We consider a Γ-equivariant principal G-bundle over S2 with structural group G a compact connected Lie group, and Γ⊂ SO(3) a finite group acting linearly on S2. We prove that the equivariant 1-skeleton X ⊂ S2 over the singular set can be classified by means of representations of their isotropy representations. Then, we show that equivariant principal G-bundles over the S2 can be classified by a Γ-fixed set of homotopy classes of maps, and the underlying G-bundle ξ over S2 can be determined by first Chern class.