nLab
circle bundle

Context

Bundles

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Definition

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

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

Examples

Revised on October 31, 2014 12:56:26 by Urs Schreiber (185.26.182.31)