= Degree of a power map of the Riemann sphere
{title2=$\deg(\zeta\mapsto\zeta^k)=k$}
For $k\ge1$, the power map has $k$ distinct preimages of every nonzero finite <regular value>, all with positive local <degree of a map between oriented manifolds>. Integrating the <pullback of a differential form> of $\Omega=i\,d\zeta\wedge d\bar\zeta/(1+|\zeta|^2)^2$ gives the same answer, since $\int\Omega=2\pi$ and $\int f^*\Omega=2\pi k$. For $k=0$ use the constant extension $1$ at infinity; its <degree of a map between oriented manifolds> is zero.
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