Projective bundle formula for complex vector bundles
= Projective bundle formula for complex vector bundles
{title2=$H^*(\mathbb P(E))$}
For a rank-$r$ complex <vector bundle> and $u=c_1(\lambda^*)$, the <cohomology> of its <projective bundle> is free over the <cohomology> of the base on $1,u,\ldots,u^{r-1}$. Consequently pullback is injective, which yields the <splitting principle for complex vector bundles> by iteration.