Sphere maps of arbitrary integer degree
= Sphere maps of arbitrary integer degree
{title2=$f_{n,m}=S^{n-1}(z\mapsto z^m),\quad n\geq1$}
Every integer $m$ is the <mapping degree> of a <continuous map> $S^n\to S^n$ in every dimension $n\geq1$. Start with the <circle> map $z\mapsto z^m$, whose argument winds $m$ times, and use <degree under suspension> repeatedly. Negative $m$ reverses the winding, and $m=0$ is constant before suspending. The <degrees of maps of the zero-sphere> are a genuine exceptional case.