nLab
universal complex line bundle

Contents

Idea

The universal complex line bundle is the complex universal vector bundle of rank 1, hence the complex line bundle which is associated to the circle group-universal principal bundle EU(1)E U(1) over the classifying space BU(1)B U(1) via the canonical action of U(1)U(1) on \mathbb{C}.

Its pullback bundle along the canonucl inclusion S 2BU(1)S^2 \longrightarrow B U(1) (the map which represents 1π 2(BU(1))1 \in \pi_2(B U(1)) \simeq \mathbb{Z}) is the basic complex line bundle on the 2-sphere.

Revised on June 6, 2017 07:28:40 by Urs Schreiber (88.77.226.246)