no. 2
Glasner’s problem for Polish groups with metrizable universal minimal flow
[Le problème de Glasner pour les groupes polonais dont le flot minimal universel est métrisable]
Nguyen Van Thé, Lionel1
1 Aix Marseille Univ, CNRS Centrale Marseille, I2M UMR 7373 13453 Marseille (France)
Annales de l'Institut Fourier, Tome 69 (2019) no. 2, pp. 941-953.

Un problème dû à Glasner, et désormais connu sous de nom de problème de Glasner, demande s’il existe un groupe polonais, minimalement presque périodique et monothétique, qui n’est pas extrêmement moyennable. Le but de cette courte note est d’observer qu’une réponse négative s’obtient sous l’hypothèse supplémentaire de la métrisablité du flot minimal universel.

Avertissement :

Suite à une erreur d’édition, la référence [13] est erronée dans le PDF. Elle aurait dû être :

[13] Nguyen Van Thé, Lionel On a problem of Specker about Euclidean representations of finite graphs (2017) (https://arxiv.org/abs/0810.2359, to appear in Expo. Math.)

A problem of Glasner, now known as Glasner’s problem, asks whether there exists a minimally almost periodic, monothetic, Polish group that is not extremely amenable. The purpose of this short note is to observe that a negative answer is obtained under the additional assumption that the universal minimal flow is metrizable.

Disclaimer:

Due to an editorial error, the citation [13] is wrong in the PDF. It should read:

[13] Nguyen Van Thé, Lionel On a problem of Specker about Euclidean representations of finite graphs (2017) (https://arxiv.org/abs/0810.2359, to appear in Expo. Math.)

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DOI : 10.5802/aif.3262
Classification : 37B05, 03C1522F5054H20
Keywords: Glasner’s problem, Minimal almost periodicity, Bohr compactification
Mot clés : Problème de Glasner, presque périodicité minimale, compactification de Bohr
Nguyen Van Thé, Lionel 1

1 Aix Marseille Univ, CNRS Centrale Marseille, I2M UMR 7373 13453 Marseille (France)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Nguyen Van Thé, Lionel. Glasner’s problem for Polish groups with metrizable universal minimal flow. Annales de l'Institut Fourier, Tome 69 (2019) no. 2, pp. 941-953. doi : 10.5802/aif.3262. https://aif.centre-mersenne.org/articles/10.5802/aif.3262/

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