Any thoughts on this problem:
If $M$ and $N$ are simply-connected, $n$-dimensional manifolds, then $H^n(M;\mathbb{Z}) \cong \mathbb{Z} \cong H^n(N;\mathbb{Z})$. A map $f:M \to N$ induces a map $f^*:H^n(N;\mathbb{Z}) \to H^n(M;\mathbb{Z})$, which is to say: $f^*:\mathbb{Z} \to \mathbb{Z}$. Any such map is given by multiplication by an integer $d$, and this integer is known as the degree of $f$, denoted by $deg(f)$. I have 2 questions:
(1) Let $f:\mathbb{C}P^2 \to \mathbb{C}P^2$. is it possible that $deg(f)=8$? is it possible that $deg(f)=9$? what can you say about the degree of $f$.
(2) what can you say about the degree of $f:\mathbb{C}P^n \to \mathbb{C}P^n$.
I know that we need to use the generators for each cohomology rings, but that is my issue I'm having trouble with this kind of questions. any help is appreciated. thanx in advance.