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 $E U(1)$ over the classifying space $B U(1)$ via the canonical action of $U(1)$ on $\mathbb{C}$.

Its pullback bundle along the canonucl inclusion $S^2 \longrightarrow B U(1)$ (the map which represents $1 \in \pi_2(B U(1)) \simeq \mathbb{Z}$) 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)