Around rational functions invertible in radicals

Abstract

A class of rational functions characterized by some wonderful properties is studied. The properties that identify this class include simple algebra (their inverses can be expressed in radicals), simple topology (the total space of the minimal Galois covering dominating them has genus 0 or 1) and simple local topol- ogy (branching data). Explicit formulae for these functions are obtained as well as their classification up to different equivalence relations.