Complex projective plane has no nontrivial covering quotient
= Complex projective plane has no nontrivial covering quotient
The <Complex projective plane> is simply connected. If it were the total space of a covering of degree at least two, it would be the <universal cover> and have a nonidentity <deck transformation>. Such a transformation acts by $u\mapsto\pm u$ on $H^*(\mathbb{CP}^2)=\mathbb Z[u]/(u^3)$, giving <Lefschetz number> 1 or 3. It therefore has a fixed point, impossible for a nonidentity deck transformation.