Conservative polynomials and yet another action of Gal( ¯/) on plane trees
Journal de Théorie des Nombres de Bordeaux, Volume 20 (2008) no. 1, pp. 205-218.

In this paper we study an action D of the absolute Galois group Γ=Gal( ¯/) on bicolored plane trees. In distinction with the similar action provided by the Grothendieck theory of “Dessins d’enfants” the action D is induced by the action of Γ on equivalence classes of conservative polynomials which are the simplest examples of postcritically finite rational functions. We establish some basic properties of the action D and compare it with the Grothendieck action.

Dans cet article nous étudions une action D du groupe de Galois absolu Γ=Gal( ¯/) sur des arbres planaires bicolores. A l’encontre de l’action similaire fournie par la théorie des “dessins d’enfants” de Grothendieck, l’action D est induite par l’action de Γ sur des classes d’équivalence de polynômes conservateurs qui sont les exemples les plus simples de fonctions rationnelles finies postcritiques. Nous établissons les propriétés principales de l’action D et la comparons avec l’action de Grothendieck.

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Published online:
DOI: 10.5802/jtnb.622
Fedor Pakovich 1

1 Department of Mathematics Ben Gurion University Beer Sheva 84105 P.O.B. 653, , Israel
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Fedor Pakovich. Conservative polynomials and yet another action of $\operatorname{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$ on plane trees. Journal de Théorie des Nombres de Bordeaux, Volume 20 (2008) no. 1, pp. 205-218. doi : 10.5802/jtnb.622. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.622/

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