Classification of equivariant vector bundles over real projective plane
Group Theory
2011-03-15 v1 Algebraic Topology
K-Theory and Homology
Representation Theory
Abstract
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.
Cite
@article{arxiv.1103.2494,
title = {Classification of equivariant vector bundles over real projective plane},
author = {Min Kyu Kim},
journal= {arXiv preprint arXiv:1103.2494},
year = {2011}
}