Prime-degree sphere map forces primary torsion
= Prime-degree sphere map forces primary torsion
If $S^n\to N$ has prime degree $p$ and $N$ is a closed connected oriented $n$-manifold, every <integral homology> group of $N$ in degrees strictly between zero and $n$ is a finite $p$-primary <abelian group>. Consequently one power of $p$ annihilates all these groups. The proof combines <Poincare duality> over each field $\mathbb F_q$, $q\ne p$, with the <universal coefficient theorem for homology> and finite generation.