Universal minimal flows of generalized Ważewski dendrites

Abstract

We study universal minimal flows of the homeomorphism groups of generalized Ważewski dendrites $W_P$, $P\subset \{3,4,\dots ,\omega \}$. If $P$ is finite, we prove that the universal minimal flow of of the homeomorphism group $H(W_P)$ is metrizable and we compute it explicitly. This answers a question of B. Duchesne. If $P$ is infinite, we show that the universal minimal flow of $H(W_P)$ is not metrizable. This provides examples of topological groups which are Roelcke precompact and have a non-metrizable universal minimal flow with a comeager orbit.

final version, accepted to the Journal of Symbolic Logic

References in corpus (1)

• Finite trees are Ramsey under topological embeddings

Cited by in corpus (9)

• Group actions on treelike compact spaces
• Automorphism groups and Ramsey properties of sparse graphs
• Maximally highly proximal flows
• Topological properties of Wazewski dendrite groups
• Universal minimal flows of homeomorphism groups of high-dimensional manifolds are not metrizable
• The weak Ramsey property and extreme amenability
• A group with Property (T) acting on the circle
• Twenty years of Nešetřil's classification programme of Ramsey classes
• On invariant means and pre-syndetic subgroups