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Simplicity of Neretin's group of spheromorphisms

Christophe Kapoudjian (1999)

Annales de l'institut Fourier

Denote by 𝒯 n , n 2 , 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.

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