## Journal of Mathematics of Kyoto University

### 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].

#### Article information

Source
J. Math. Kyoto Univ., Volume 41, Number 3 (2001), 517-534.

Dates
First available in Project Euclid: 17 August 2009

https://projecteuclid.org/euclid.kjm/1250517616

Digital Object Identifier
doi:10.1215/kjm/1250517616

Mathematical Reviews number (MathSciNet)
MR1878719

Zentralblatt MATH identifier
1149.57317

#### Citation

Cho, Jin-Hwan; Kim, Sung Sook; Masuda, Mikiya; Suh, Dong Youp. Classification of equivariant complex vector bundles over a circle. J. Math. Kyoto Univ. 41 (2001), no. 3, 517--534. doi:10.1215/kjm/1250517616. https://projecteuclid.org/euclid.kjm/1250517616