What are the Stiefel-Whitney classes of complex projective spaces?



Stiefel-Whitney class
It follows from the Whitney sum formula that $c(T\_{\mathbf{C}P^n}) = (1+z)^{n+1}$, where $z \in H^2(\mathbf{C}P^n,\mathbf{Z})$ is the generator corresponding to the canonical bundle. (I assume you meant the Chern classes; for the Stiefel-Whitney of a complex vector bundle restricted to a real vector bundle, $w\_{2i}$ is the mod-$2$ reduction of $c\_i$; and for the odd Stiefel-Whitney classes note that $H^{2i+1}(\mathbf{C}P^n) = 0$)


