Return to Revisions

By the way, a very cool (to my mind) way of computing the Euler characteristic of $\mathbb{C}P^n$ is to treat it as the $n$-fold symmetric product of $\mathbb{C}P^1 = \mathbb{S}^2$ with itself. Then, it is apparently a result of MacDonald (of Atiyah and M fame) that the Euler characteristic of an $n$-fold symmetric product of a space $X$ with itself equals $\binom{\chi(X)+n-1}{\chi(X) - 1}.$`