nLab circle bundle

Contents

Context

Bundles

bundles

Context

Classes of bundles

Universal bundles

Presentations

Examples

Constructions

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

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