nLab circle principal bundle

Definition

A circle group-principal bundle, a principal U(1)-bundle (see there for more).

Properties

Relation to complex line bundles

Under the standard linear representation of $U(1)$ on the complex numbers the associated bundle to a $U(1)$-principal bundle is a complex line bundle.

Related concepts

• circle action

• circle n-bundle with connection

• the classifying space is infinite complex projective space

• complex oriented cohomology