Classification of equivariant vector bundles over two-torus
Group Theory
2010-07-13 v2 Algebraic Topology
K-Theory and Homology
Representation Theory
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
Cite
@article{arxiv.1005.0682,
title = {Classification of equivariant vector bundles over two-torus},
author = {Min Kyu Kim},
journal= {arXiv preprint arXiv:1005.0682},
year = {2010}
}
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45pages