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Classification of equivariant vector bundles over real projective plane

By Min Kyu Kim


We classify equivariant topological complex vector bundles over real projective plane under a compact Lie group (not necessarily effective) action. It is shown that nonequivariant Chern classes and isotropy representations at (at most) three points are sufficient to classify equivariant vector bundles over real projective plane except one case. To do it, we relate the problem to classification on two-sphere through the covering map because equivariant vector bundles over two-sphere have been already classified

Topics: Mathematics - Group Theory, Mathematics - Algebraic Topology, Mathematics - K-Theory and Homology, Mathematics - Representation Theory, Primary 57S25, 55P91, Secondary 20C99
Year: 2011
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