A Group of Automorphisms of the Rooted Dyadic Tree and Associated Gelfand Pairs

Daniele D’Angeli; Alfredo Donno

Displaying similar documents to “A Group of Automorphisms of the Rooted Dyadic Tree and Associated Gelfand Pairs”

Introduction to Iterated Monodromy Groups

Sébastien Godillon (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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The theory of iterated monodromy groups was developed by Nekrashevych [9]. It is a wonderful example of application of group theory in dynamical systems and, in particular, in holomorphic dynamics. Iterated monodromy groups encode in a computationally efficient way combinatorial information about any dynamical system induced by a post-critically finite branched covering. Their power was illustrated by a solution of the Hubbard Twisted Rabbit Problem given by Bartholdi and Nekrashevych...

Simplicity of Neretin's group of spheromorphisms

Christophe Kapoudjian (1999)

Annales de l'institut Fourier

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Denote by $𝒯_{n}$ , $n \geq 2$ , the regular tree whose vertices have valence $n + 1$ , $\partial 𝒯_{n}$ its boundary. Yu. A. Neretin has proposed a group $N_{n}$ of transformations of $\partial 𝒯_{n}$ , thought of as a combinatorial analogue of the diffeomorphism group of the circle. We show that $N_{n}$ is generated by two groups: the group $Aut (𝒯_{n})$ of tree automorphisms, and a Higman-Thompson group $G_{n}$ . We prove the simplicity of $N_{n}$ and of a family of its subgroups.