Degrees of maps factoring through real projective space
= Degrees of maps factoring through real projective space
For $n\geq2$, a self-map of $S^n$ factoring through <Real projective space> $\mathbb{RP}^n$ has degree zero when $n$ is even, and can have exactly the even degrees when $n$ is odd. In the odd case the first map lifts through the double covering and the covering has degree two. The dimension-one exception allows every integer, since $\mathbb{RP}^1\cong S^1$.