Introduction to Iterated Monodromy Groups

Sébastien Godillon

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Simplicity of Neretin's group of spheromorphisms

Christophe Kapoudjian (1999)

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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.

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Thompson's group $F (n)$ is not minimally almost convex.

Wladis, Claire (2007)

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Jaroslav Nešetřil (1972)

Commentationes Mathematicae Universitatis Carolinae

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The triangles method to build $X$ -trees from incomplete distance matrices

Alain Guénoche, Bruno Leclerc (2001)

RAIRO - Operations Research - Recherche Opérationnelle

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A method to infer $X$ -trees (valued trees having $X$ as set of leaves) from incomplete distance arrays (where some entries are uncertain or unknown) is described. It allows us to build an unrooted tree using only 2 $n$ -3 distance values between the $n$ elements of $X$ , if they fulfill some explicit conditions. This construction is based on the mapping between $X$ -tree and a weighted generalized 2-tree spanning $X$ .