Does there exist any nontrivial holomorphic vector bundle on $\mathbb{C}^n$?
I know $(1)$ Every line bundle on $\mathbb{C}^n$ is trivial, $(2)$ Every holomorphic vector bundle on $\mathbb{C}$ is trivial, (3) There exist a nontrivial line bundle on a contractible complex manifold, but I'm not sure if the above statement is true.