# Equivariant holonomy of U(1)-bundles

## TL;DR

This paper introduces the concept of equivariant holonomy for U(1)-bundles with invariant connections, generalizing classical holonomy properties to the equivariant setting and linking it to prequantization and anomaly cancellation.

## Contribution

It defines equivariant holonomy for U(1)-bundles, proves its classification power, and demonstrates its applications in geometric quantization and anomaly analysis.

## Key findings

- Equivariant holonomy classifies invariant U(1)-bundles with connection.
- The framework extends classical holonomy properties to the equivariant context.
- Applications include results in equivariant prequantization and anomaly cancellation.

## Abstract

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.