Related papers: Extremely amenable automorphism groups of countabl…

In this paper, we study a family of finitely generated elementary amenable iet-groups. These groups are generated by finitely many rationals iets and rotations. For them, we state criteria for not virtual nilpotency or solvability, and we…

This paper studies Moore's measurable cohomology theory for locally compact groups and Polish modules. An elementary dimension-shifting argument is used to show that all classes in that theory have representatives with considerable extra…

We consider groups of automorphisms of locally finite trees, and give conditions on its subgroups that imply that they are not elementary amenable. This covers all known examples of groups that are not elementary amenable and act on the…

We prove a characterization of the amenability of countable Borel equivalence relations in terms of the uniform Liouville property for group actions on their classes. Furthermore, inspired by a well-known amenability criterion for locally…

We give, for each level of complexity L, a Hurewicz-like characterization of the Borel subsets with countable sections of a product of two Polish spaces that cannot become in L by changing the two Polish topologies.

We prove that every Polish group with more than two elements admits a non-trivial topological group automorphism. As a consequence, a hypothetical uniquely homogeneous Polish space with more than two points cannot be a semitopological…

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…

By a recent result of Juh\'{a}sz and van Mill, a locally compact topological group whose dense subspaces are all separable is metrizable. In this note we investigate the following question: is every locally compact group having all dense…

It is shown that in various categories, including many consisting of maps or hypermaps, oriented or unoriented, of a given hyperbolic type, every countable group $A$ is isomorphic to the automorphism group of uncountably many non-isomorphic…

A problem of Glasner, now known as Glasner's problem, asks whether every minimally almost periodic, monothetic, Polish groups is extremely amenable. The purpose of this short note is to observe that a positive answer is obtained under the…

The goal of this article is to study results and examples concerning finitely presented covers of finitely generated amenable groups. We collect examples of groups $G$ with the following properties: (i) $G$ is finitely generated, (ii) $G$…

We show that if $G$ is an amenable topological group, then the topological group $L^{0}(G)$ of strongly measurable maps from $([0,1],\lambda)$ into $G$ endowed with the topology of convergence in measure is whirly amenable, hence extremely…

We establish that a second countable locally compact groupoid possessing a continuous Haar system is topologically amenable if and only if it is Borel amenable. We give some examples and applications.

We begin the systematic study of decision problems for finitely generated groups given by a solution to their word problem. We relate this to the study of computable analysis on the space of marked groups. We point out that several distinct…

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…

The structures $\langle M,\subseteq^M\rangle$ arising as the inclusion relation of a countable model of sufficient set theory $\langle M,\in^M\rangle$, whether well-founded or not, are all isomorphic. These structures $\langle…

A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable…

In this paper we present general techniques for characterising minimal and maximal semigroup topologies on the endomorphism monoid $\operatorname{End}(\mathbb{A})$ of a countable relational structure $\mathbb{A}$. As applications, we show…

In this paper we extend the approach of M. Cavaleri to effective amenability to the class of computably enumerable groups, i.e. in particular we do not assume that groups are finitely generated. In the case of computable groups we also…

We consider automorphism groups of some countably categorical structures and their precompact expansions. We prove that automorphism groups of omega-stable omega-categorical structures have metrizable universal minimal flows. We also study…