Conservative polynomials and yet another action of $\Gal(\bar \Q/\Q)$ on plane trees

Details Conservative polynomials and yet another action of $\Gal(\bar \Q/\Q)$ on plane trees Conservative polynomials and yet another action of $\Gal(\bar \Q/\Q)$ on plane trees

2004-04-27

arxiv.org/abs/math/0404478v3

Mathematics

Number Theory

12 pages, 9 figures, revised

Scientific paper

In this paper we study an action of the absolute Galois group $\Gamma$ on bicolored plane trees induced by the action of $\Gamma$ on equivalence classes of conservative polynomials which are the simplest example of postcritically finite rational functions. We establish some basic properties of this action and compare it with the similar action provided by the Grothendieck theory of "Dessins d'enfants".

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