Equivariant holonomy of U(1)-bundles

We define the equivariant holonomy of an invariant connection on a principal $U(1)$-bundle. The properties of the ordinary holonomy are generalized to the equivariant setting. In particular, equivariant $U(1)$-bundles with connection are shown to be classified by its equivariant holonomy modulo isomorphisms. We also show that the equivariant holonomy can be used to obtain results about equivariant prequantization and anomaly cancellation.