Related papers: Equivariant concentration in topological groups

Let $G$ be a group of homeomorphisms of a topological space $X$. $G$ is $\textit{(properly) isometrizable}$ if there exists a $G$-invariant (proper) gauge structure on $X$. $G$ is $\textit{equiregular}$ if for every $x \in X$ and every open…

In this paper we further study links between concentration of measure in topological transformation groups, existence of fixed points, and Ramsey-type theorems for metric spaces. We prove that whenever the group $\Iso(\U)$ of isometries of…

In this article it is proved, that every locally compact second countable group has a left invariant metric d, which generates the topology on G, and which is proper, ie. every closed d-bounded set in G is compact. Moreover, we obtain the…

Let $M$ be a smooth compact oriented connected manifold, and ${\rm Homeo}_0(M,\mu)$ the group of homeomorphisms of $M$ supported away from $\partial M,$ which preserve a Borel probability measure $\mu$ induced by a volume form on $M$, and…

We study the topology of the space of probability measures invariant under the geodesic flow, defined on the unit-tangent bundle of a compact Riemannian manifold with non-positive curvature. Building on a previous work by Coud\`ene and…

For each arbitrary finite group $G$, we consider a suitable notion of Gromov Hausdorff distance between compact $G$ metric spaces and derive lower bounds based on equivariant topology methods. As applications, we prove equivariant rigidity…

It is shown that a topological group G is topologically isomorphic to the isometry group of a (complete) metric space iff G coincides with its G-delta-closure in the Rajkov completion of G (resp. if G is Rajkov-complete). It is also shown…

This paper concerns Gibbs measures $\nu$ for some nonlinear PDE over the $D$-torus ${\bf T}^D$. The Hamiltonian $H=\int_{{\bf T}^D} \Vert\nabla u\Vert^2 - \int_{{\bf T}^D} \vert u\vert^p$ has canonical equations with solutions in…

Let $M$ be a compact $n$-dimensional Riemanian manifold, End($M$) the set of the endomorphisms of $M$ with the usual $\mathcal{C}^0$ topology and $\phi: M\to\mathbb{R}$ continuous. We prove that there exists a dense subset of $\mathcal{A}$…

We study the set S of ergodic probability Borel measures on stationary non-simple Bratteli diagrams which are invariant with respect to the tail equivalence relation. Equivalently, the set S is formed by ergodic probability measures…

We prove that if $G$ is a countable discrete group with property (T) over an infinite subgroup $H<G$ which contains an infinite Abelian subgroup or is normal, then $G$ has continuum many orbit inequivalent measure preserving a.e. free…

The Hilbert-Smith conjecture states, for any connected topological manifold $M$, any locally compact subgroup of $\mathrm{Homeo}(M)$ is a Lie group. We generalize basic results of Segal-Kosniowski-tomDieck (2.6), James-Segal (2.12), G…

We establish an induction isomorphism in the context of measurable bounded cohomology of discrete measured groupoid, which generalizes the Eckmann-Shapiro isomorphism in bounded cohomology of lattices due to Burger and Monod. In our wider…

Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of countably infinite structures, that are…

We adapt a construction of Gabrielov and Vorobjov for use in the symmetric case. Gabrielov and Vorobjov had developed a means by which one may replace an arbitrary set $S$ definable in some o-minimal expansion of $\mathbb{R}$ with a compact…

We show that for any co-amenable compact quantum group A=C(G) there exists a unique compact Hausdorff topology on the set EA of isomorphism classes of ergodic actions of G such that the following holds: for any continuous field of ergodic…

This is the second of two papers but has been written so as to have minimal dependence on the first paper (which is also on this archive). Let G be a group and let M be a CAT(0) proper metric space (e.g. a simply connected complete…

We mainly discuss the cardinal invariants and generalized metric properties on paratopological groups or rectifiable spaces, and show that: (1) If $A$ and $B$ are $\omega$-narrow subsets of a paratopological group $G$, then $AB$ is…

We present a simple approach to questions of topological orbit equivalence for actions of countable groups on topological and smooth manifolds. For example, for any action of a countable group $\Gamma$ on a topological manifold where the…

Here we shall consider the topology and dynamics associated to a wide class of matchbox manifolds, including a large selection of tiling spaces and all minimal matchbox manifolds of dimension one. For such spaces we introduce topological…