2010/05/05 by Kim, Min Kyu
#20C99 #55P91 #57S25 #FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1005.0681
We exhaustively classify topological equivariant complex vector bundles over two-sphere under a compact Lie group (not necessarily effective) action. It is shown that inequivariant Chern classes and isotropy representations at (at most) three points are sufficient to classify equivariant vector bundles except a few cases. To do it, we calculate equivariant homotopy of the set of equivariant clutching maps. Holomorphic version of this will be treated in other paper. Classification on two-torus, real projective plane, Klein bottle will appear soon.