Related papers: Topological dynamics and definable groups

We give examples of groups G such that G^00 is different from G^000. We also prove that for groups G definable in an o-minimal structure, G has a "bounded orbit" iff G is definably amenable. These results answer questions of Gismatullin,…

This article will explore the K- and L-theory of group rings and their applications to algebra, geometry and topology. The Farrell-Jones Conjecture characterizes K- and L-theory groups. It has many implications, including the Borel and…

In this paper, we discuss function theory on Teichm\"uller space through Thurston's theory, as well as the dynamics of subgroups of the mapping class group of a surface, with reference to Sullivan's theory on the ergodic actions of discrete…

We study canonical quotients in model theory, mainly stable quotients of type-definable groups and invariant types in NIP theories. We extend the modelling property to continuous theories and use it to study $n$-dependence in hyperdefinable…

Given a smooth partial action $\alpha$ of a Lie groupoid $G$ on a smooth manifold $M,$ we provide necessary and sufficient conditions for $\alpha$ to be globalizable with smooth globalization. As an application, we provide results on the…

We continue the study of a class of topological $\mathcal{L}$-fields endowed with a generic derivation $\delta$, focussing on describing definable groups. We show that one can associate to an $\mathcal{L}_{\delta}$ definable group a type…

Consider the pair $(G,P)$ consisting of an abelian lattice-ordered discrete group $G$ and its positive cone $P$. Let $\alpha$ be an action of $P$ by extendible endomorphisms of a $C^*$-algebra $A$. We show that the Nica-Toeplitz algebra…

The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…

Structure constants of the $su(N)$ ($N$ odd) Lie algebras converge when N goes to infinity to the structure constants of the Lie algebra {\it sdiff}$(T^2)$ of the group of area-preserving diffeomorphisms of a 2D torus. Thus Zeitlin and…

Given an action by a finite quantum group $\mathbb{G}$ on a von Neumann algebra $M$, we prove that a number of familiar $W^*$ properties are equivalent for $M$ and the fixed-point algebra $M^{\mathbb{G}}$ (i.e. hold or not simultaneously…

We consider the homotopical dynamics on compact orientable surfaces of positive genus g. We establish a sufficient and necessary algebraic criterion for homotopy classes with infinitely many periodic points of maps on such surfaces in terms…

We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups $G$ such that every element of $G$ is contained in a compact open normal subgroup of $G$. For…

The fields nonlinear modes quantization scheme is discussed. New form of the perturbation theory achieved by unitary mapping the quantum dynamics in the space $W_G$ of (action, angle)-type collective variables. It is shown why the…

We define and study notions of amenability and skew-amenability of continuous actions of topological groups on compact topological spaces. Our main motivation is the question under what conditions amenability of a topological group passes…

We construct analogues of FI-modules where the role of the symmetric group is played by the general linear groups and the symplectic groups over finite rings and prove basic structural properties such as Noetherianity. Applications include…

We extend the duality theory for topological groups from the classical theory for compact Lie groups, via the topological study by J. R. Klein [Kl01] and the p-complete study for p-compact groups by T. Bauer [Ba04], to a general duality…

We show that every fsg group externally definable in an NIP structure is definably isomorphic to a group interpretable in it. Our proof relies on honest definitions and a group chunk result reconstructing a hyper-definable group from its…

To a "stable homotopy theory" (a presentable, symmetric monoidal stable $\infty$-category), we naturally associate a category of finite \'etale algebra objects and, using Grothendieck's categorical machine, a profinite group that we call…

In this paper, we study several finite approximation properties of topological full groups of group actions on the Cantor set such that free points are dense. Firstly, we establish that for such a distal action $\alpha$ of a countable…

We note a parallel between some ideas of stable model theory and certain topics in finite combinatorics related to the sum-product phenomenon. For a simple linear group G, we show that a finite subset X with |X X \^{-1} X |/ |X| bounded is…