Geodesic
Fields of definition of rational functions of one variable with three critical values
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 3, pp. 781-799.

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Rational functions of one complex variable with three critical values are considered. According to Grothendieck theory, such functions are classified by the isotopic classes of the connected spherical graphs. By a suitable fractional-linear variable substitution these coefficients can be transformed to algebraic numbers. The paper is devoted to the problem of minimization of irrationality degrees of these coefficients. 
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V. O. Filimonenkov; G. B. Shabat. Fields of definition of rational functions of one variable with three critical values. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 3, pp. 781-799. http://geodesic.mathdoc.fr/item/FPM_1995_1_3_a13/

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