universal complex line bundle



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 (