English

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

Keywords

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}
}

Comments

45pages

R2 v1 2026-06-21T15:18:41.737Z