Classification of equivariant real vector bundles over a circle

Abstract

This is a continuation of the previous work [CKMS01] by the authors on classification of equivariant complex vector bundles over a circle. In this paper equivariant real vector bundles over a circle with a compact Lie group action are classified, by characterizing their fiber representations, and by using the result of the complex case. Their triviality is also treated. The basic phenomenon is similar to the complex case but more complicated here.