Classification of equivariant vector bundles over two-torus

2010/05/05 by Kim, Min Kyu
#19L47 #20C99 #55P91 #57S25 #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1005.0682

Abstract

We exhaustively classify topological equivariant complex vector bundles over two-torus under a compact Lie group (not necessarily effective) action. It is shown that inequivariant Chern classes and isotropy representations at (at most) six points are sufficient to classify equivariant vector bundles except a few cases. To do it, we calculate homotopy of the set of equivariant clutching maps. And, classification on real projective plane, Klein bottle will appear soon

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