A realizability criterion for rational maps with three branch points

Zhiqiang Wei

Let \[ π_{0}=[\underbrace{2,\ldots,2}_{2s-1}],\quad π_{\infty}=[\underbrace{3,\ldots,3}_{s},\underbrace{1,\ldots,1}_{s-2}],\quad π_{1}=[γ_{1},γ_{2},γ_{3}] \] be three nontrivial pa…