# nLab circle bundle

### Context

#### Bundles

bundles

fiber bundles in physics

cohomology

# Contents

## Definition

A circle bundle is a principal bundle for the circle group $S^1$. Equivalently this is a $U(1)$-principal bundle, for the unitary group $U(1)$.

Under the canonical representation $\mathbf{B}U(1) \to Vect_{\mathbb{C}}$ the corresponding associated bundle is a complex line bundle.

## Examples

Last revised on October 31, 2014 at 12:56:26. See the history of this page for a list of all contributions to it.