Simplicity of Neretin's group of spheromorphisms

Kapoudjian, Christophe

doi:10.5802/aif.1715

Cited by 34 publications

(37 citation statements)

References 5 publications

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“…It can also be described as a certain group of homeomorphisms of a Cantor set [5, p. 57]. Moreover, one can view G q,r as a subgroup of G q,2 and the latter as a group acting spheromorphically on the (q + 1)-regular tree [25,Section 2.2], that is, they are subgroups of N q . If q is even, then G q,r = G q,r .…”

Section: śWiatos Law R Gal and Jakub Gismatullinmentioning

confidence: 99%

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Uniform simplicity of groups with proximal action

Gal

Gismatullin

2017

Trans. Amer. Math. Soc. Ser. B

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Abstract. We prove that groups acting boundedly and order-primitively on linear orders or acting extremely proximally on a Cantor set (the class including various Higman-Thomson groups; Neretin groups of almost automorphisms of regular trees, also called groups of spheromorphisms; the groups of quasi-isometries and almost-isometries of regular trees) are uniformly simple. Explicit bounds are provided.

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Section: śWiatos Law R Gal and Jakub Gismatullinmentioning

confidence: 99%

“…The group N q was introduced by Neretin in [27, 4.5, 3.4] as the group AAut(T q ) of spheromorphisms of the (q + 1)-regular tree T q . It is abstractly simple [25].…”

Section: Groups Almost Acting On Treesmentioning

confidence: 99%

Uniform simplicity of groups with proximal action

Gal

Gismatullin

2017

Trans. Amer. Math. Soc. Ser. B

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“…Neretin proved that, from the point of view of representation theory, the group N d can be seen as a p-adic analogue of the diffeomorphism group of the circle. Inspired by a simplicity result for the diffeomorphism group of the circle Diff + (S 1 ) [21], Kapoudjian later proved that the group N d is abstractly simple [23].…”

Section: Introduction Almost Automorphism Groupsmentioning

confidence: 99%

Compact presentability of tree almost automorphism groups

Boudec¹

2017

Annales De l'Institut Fourier

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We establish compact presentability, i.e. the locally compact version of finite presentability, for an infinite family of tree almost automorphism groups. Examples covered by our results include Neretin's group of spheromorphisms, as well as the topologically simple group containing the profinite completion of the Grigorchuk group constructed by Barnea, Ershov and Weigel.We additionally obtain an upper bound on the Dehn function of these groups in terms of the Dehn function of an embedded Higman-Thompson group. This, combined with a result of Guba, implies that the Dehn function of the Neretin group of the regular trivalent tree is polynomially bounded.

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“…groups are the groups of almost automorphisms of trees introduced by Yu. Neretin, [25,26], and shown to be simple by C. Kapoudjian, [27]. Neretin groups are also studied in [28], where it is shown that they do not contain a lattice, and the notation used here conforms with that paper.…”

Section: Glöckner Bases This Decomposition On a Variation On ([18] Lementioning

confidence: 75%

Computing the Scale of an Endomorphism of a totally Disconnected Locally Compact Group

Willis

2017

Axioms

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Abstract:The scale of an endomorphism of a totally disconnected, locally compact group G is defined and an example is presented which shows that the scale function is not always continuous with respect to the Braconnier topology on the automorphism group of G. Methods for computing the scale, which is a positive integer, are surveyed and illustrated by applying them in diverse cases, including when G is compact; an automorphism group of a tree; Neretin's group of almost automorphisms of a tree; and a p-adic Lie group. The information required to compute the scale is reviewed from the perspective of the, as yet incomplete, general theory of totally disconnected, locally compact groups.

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Simplicity of Neretin's group of spheromorphisms

Cited by 34 publications

References 5 publications

Uniform simplicity of groups with proximal action

Uniform simplicity of groups with proximal action

Compact presentability of tree almost automorphism groups

Computing the Scale of an Endomorphism of a totally Disconnected Locally Compact Group

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