Simplicity of Neretin's group of spheromorphisms
Annales de l'Institut Fourier, Volume 49 (1999) no. 4, pp. 1225-1240.

Denote by 𝒯 n , n2, the regular tree whose vertices have valence n+1, 𝒯 n its boundary. Yu. A. Neretin has proposed a group N n of transformations of 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.

Notons 𝒯 n , n2, l’arbre régulier dont les sommets sont de valence n+1, 𝒯 n son bord. Yu. A. Neretin a proposé, comme analogue combinatoire du groupe des difféomorphismes du cercle, un groupe de transformations N n agissant sur 𝒯 n . On montre que N n est engendré par deux groupes: le groupe Aut (𝒯 n ) des automorphismes de l’arbre, et un groupe de Higman-Thompson G n . On prouve la simplicité de N n et d’une famille de ses sous-groupes.

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Kapoudjian, Christophe. Simplicity of Neretin's group of spheromorphisms. Annales de l'Institut Fourier, Volume 49 (1999) no. 4, pp. 1225-1240. doi : 10.5802/aif.1715. https://aif.centre-mersenne.org/articles/10.5802/aif.1715/

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