Group actions on treelike compact spaces

E Glasner, M Megrelishvili - Science China Mathematics, 2019 - Springer
We show that group actions on many treelike compact spaces are not too complicated
dynamically. We first observe that an old argument of Seidler (1990) implies that every …

Bounded cohomology of groups acting on Cantor sets

K Andritsch - arXiv preprint arXiv:2210.00459, 2022 - arxiv.org
We study the bounded cohomology of certain groups acting on the Cantor set. More
specifically, we consider the full group of homeomorphisms of the Cantor set as well as …

Structural properties of dendrite groups

B Duchesne, N Monod - Transactions of the American Mathematical …, 2019 - ams.org
Let $ G $ be the homeomorphism group of a dendrite. We study the normal subgroups of $ G
$. For instance, there are uncountably many non-isomorphic such groups $ G $ that are …

Group action with finite orbits on local dendrites

EHE Abdalaoui, I Naghmouchi - Dynamical Systems, 2021 - Taylor & Francis
It is shown that the restriction of the action of any group with finite orbit on the minimal sets of
local dendrites is equicontinuous. Consequently, we obtain that the action of any amenable …

Topological dynamics of kaleidoscopic groups

G Basso, T Tsankov - Advances in Mathematics, 2023 - Elsevier
Kaleidoscopic groups are a class of permutation groups recently introduced by Duchesne,
Monod, and Wesolek. Starting with a permutation group Γ, the kaleidoscopic construction …

The cup product of Brooks quasimorphisms

M Bucher, N Monod - Forum Mathematicum, 2018 - degruyter.com
The cup product of Brooks quasimorphisms Skip to content Should you have institutional
access? Here's how to get it ... De Gruyter € EUR - Euro £ GBP - Pound $ USD - Dollar EN …

Topological properties of Ważewski dendrite groups

B Duchesne - Journal de l'École polytechnique-Mathématiques, 2020 - numdam.org
Homeomorphism groups of generalized Ważewski 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 …

A closed subgroup of the homeomorphism group of the circle with property (T)

B Duchesne - International Mathematics Research Notices, 2023 - academic.oup.com
We exhibit a topological group with property (T) acting nonelementarily and continuously on
the circle. This group is an uncountable totally disconnected closed subgroup of. It has a …

[PDF][PDF] On recurrence in dendrite flows

H Hattab - Results in Nonlinear Analysis, 2024 - nonlinear-analysis.com
A continuous action of a topological group G on a compact topological space X is called a
flow (G, X). Particular attention was paid to the study of groups acting on dendrites [14, 10 …

Some examples of tame dynamical systems answering questions of Glasner and Megrelishvili

A Codenotti - arXiv preprint arXiv:2305.00726, 2023 - arxiv.org
Glasner and Megrelishvili proved that every continuous action of a topological group $ G $
on a dendrite $ X $ is tame. We produce two examples of an action on a dendrite which is …