Related papers: Cost of inner amenable groupoids

We establish a characterization of extreme amenability of any Polish group in Fra\"iss\'e-theoretic terms in the setting of continuous logic, mirroring a theorem due to Kechris, Pestov and Todorcevic for closed subgroups of the permutation…

We show that the group of bounded automatic automorphisms of a rooted tree is amenable, which implies amenability of numerous classes of groups generated by finite automata. The proof is based on reducing the problem to showing amenability…

The groups G_{k,1} of Richard Thompson and Graham Higman can be generalized in a natural way to monoids, that we call M_{k,1}, and to inverse monoids, called Inv_{k,1}; this is done by simply generalizing bijections to partial functions or…

Johnson's characterization of amenable groups states that a discrete group $\Gamma$ is amenable if and only if $H_b^{n \geq 1}(\Gamma; V) = 0$ for all dual normed $\mathbb{R}[\Gamma]$-modules V. In this paper, we extend the previous result…

We prove an analogue of the fixed-point theorem for the case of definably amenable groups.

We consider the amenability of groupoids $G$ equipped with a group valued cocycle $c:G\to Q$ with amenable kernel $c^{-1}(e)$. We prove a general result which implies, in particular, that $G$ is amenable whenever $Q$ is amenable and if…

We prove that many properties and invariants of definable groups in NIP theories, such as definable amenability, G/G^{00}, etc., are preserved when passing to the theory of the Shelah expansion by externally definable sets, M^{ext}, of a…

It is proved that a discrete group G is exact if and only if its left translation action on the Stone-Cech compactification is amenable. Combining this with an unpublished result of Gromov, we have the existence of non exact discrete…

Entropy of measure preserving or continuous actions of amenable discrete groups allows for various equivalent approaches. Among them are the ones given by the techniques developed by Ollagnier and Pinchon on the one hand and the…

In a stable theory, a stationary type $q \in S(A)$ internal to a family of partial types $\mathcal{P}$ over $A$ gives rise to a type-definable group, called its binding group. This group is isomorphic to the group…

For a locally compact group $G$, let $A(G)$ denote its Fourier algebra, $M_{cb}(A(G))$ the completely bounded multipliers of $A(G)$, and $A_{M_cb}(G)$ the closure of $A(G)$ in $M_{cb}(A(G))$. We show that, if $A_{M_cb}(G)$ is amenable, then…

We study topological groups $G$ for which the universal minimal $G$-system $M(G)$, or the universal irreducible affine $G$-system $IA(G)$ are tame. We call such groups intrinsically tame and convexly intrinsically tame. These notions are…

We describe sofic groupoids in elementary terms and prove several permanence properties for sofcity. We show that sofcity can be determined in terms of the full group alone, answering a question by Conley, Kechris and Tucker-Drob.

Petersen and Tenner defined the depth statistic for Coxeter group elements which, in the symmetric group, can be described in terms of a cost function on transpositions. We generalize that cost function to the other classical (finite and…

For every infinite (countable discrete) amenable group $G$ and every positive integer $d$ we construct a minimal $G$-action of mean dimension $d/2$ which cannot be embedded in the full $G$-shift on $([0,1]^d)^G$.

Let $\Gamma$ be an amenable countable discrete group. Fix an ergodic free nonsingular action of $\Gamma$ on a nonatomic standard probability space. Let $G$ be a compactly generated locally compact second countable group such that the…

Consider the following property of a topological group G: every continuous affine G-action on a Hilbert space with a bounded orbit has a fixed point. We prove that this property characterizes amenability for locally compact sigma-compact…

A rigidity theory is developed for the Euclidean and non-Euclidean placements of countably infinite simple graphs in R^d with respect to the classical l^p norms, for d>1 and 1<p<\infty. Generalisations are obtained for the Laman and…

It is a long standing open problem whether the Thompson group $F$ is an amenable group. In this paper we show that if $A$, $B$, $C$ denote the standard generators of Thompson group $T$ and $D:=C B A^{-1}$ then…

This paper is devoted to a study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. Uncertainty is modelled by a (possibly uncountable) family of price processes on the same probability space. Our…