circle principal bundle (changes) in nLab

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Contents

Definition

A circle group-principal bundle.

Properties

Relation to complex line bundles

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

• circle action

• circle n-bundle with connection

• the classifying space is infinite complex projective space

• complex oriented cohomology