Let $\pi:\mathbb{C}^{n}\setminus{O}\rightarrow\mathbb{CP}^{n-1}, n\geq 3$, if we pull back the tangent bundle of $\mathbb{CP}^{n-1}$ we would get a nontrivial bundle over $\mathbb{C}^{n}\setminus{O}$. Now my question would be: what is $H^{1}(\mathbb{C}^{n}\setminus{O},\pi^{*}\mathcal{T}_{\mathbb{CP}^{n}})$?