Article Dans Une Revue Journal de l'École polytechnique — Mathématiques Année : 2020

Topological properties of Wazewski dendrite groups

Résumé

Homeomorphism groups of generalized Wazewski dendrites act on the infinite countable set of branch points of the dendrite and thus have a nice Polish topology. In this paper, we study them in the light of this Polish topology. The group of the universal Wazewski dendrite D is more characteristic than the others because it is the unique one with a dense conjugacy class. For this group G, we show some of its topological properties like existence of a comeager conjugacy class, the Steinhaus property, automatic continuity and the small index subgroup property. Moreover, we identify the universal minimal flow of G. This allows us to prove that point-stabilizers in G are amenable and to describe the universal Furstenberg boundary of G.

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hal-02066642 , version 1 (13-03-2019)
hal-02066642 , version 2 (06-07-2020)

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Bruno Duchesne. Topological properties of Wazewski dendrite groups. Journal de l'École polytechnique — Mathématiques, 2020, 7, pp.431-477. ⟨10.5802/jep.121⟩. ⟨hal-02066642v2⟩
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