Classification of equivariant complex vector bundles over a circle

Abstract

In this paper we characterize the fiber representations of equivariant complex vector bundles over a circle and classify these bundles. We also treat the triviality of them by investigating the extensions of the fiber representations. As a corollary of our results, we calculate the reduced equivariant $K$-group of a circle for any compact Lie group, which extends a result of Y. Yang [Yan95].