Genus monotonicity under nonzero-degree surface maps
= Genus monotonicity under nonzero-degree surface maps
{title2=$\deg f\ne0\implies g(M)\ge g(N)$}
For a <continuous map> of nonzero <mapping degree> between closed connected oriented surfaces, <rational cohomology injectivity of a nonzero-degree map> gives an injection on $H^1$. Since the first <Betti number> of an oriented surface of genus $g$ is $2g$, the source genus is at least the target genus.