2
votes
1answer
78 views

a question about space of smooth sections

Let $\Gamma(M,L) $ be the space of smooth sections, then why $\Gamma(M,L) $ is isomorphic to $A=\{f:L^{\times}\to \mathbb{C}; f(cz)=c^{-1}f(z), c\in \mathbb{C}-\{0\} , z\in L^{\times}\}$ . Here ...
1
vote
0answers
70 views

Principal $G$-bundles as pull back bundles.

Let $G$ be a compact Lie group and consider a $G$-universal bundle $\pi: EG \to BG $ where $BG$ is the classifying space for the goup $G$ and the bundle $\pi: EG \to BG $ is defined as the principal ...
2
votes
2answers
101 views

Universal property of universal bundles.

A classifying space for a group $G$ is a topological space $BG$ with a principle $G$-bundle $p : EG \to BG$ where $EG$ is contractile, so that $BG = EG/G$. A classifying space is universal in the ...