Classification of equivariant vector bundles over two-torus

Details Classification of equivariant vector bundles over two-torus Classification of equivariant vector bundles over two-torus

2010-05-05

arxiv.org/abs/1005.0682v2

Mathematics

Group Theory

45pages

Scientific paper

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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