Related papers: Jordan property for homeomorphism groups and almos…

We prove that, for a free action $\alpha \colon G \curvearrowright X$ of a countably infinite discrete amenable group on a compact metric space, the small boundary property is implied by uniform property $\Gamma$ of the Cartan subalgebra…

Using a m\'elange of techniques at the rich intersection of deformation/rigidity theory, finite index subfactor theory, and geometric group theory, we prove the existence of a continuum of property (T) factors that are pairwise non-stably…

We first obtain finiteness properties for the collection of closed normal subgroups of a compactly generated locally compact group. Via these properties, every compactly generated locally compact group admits an essentially chief series -…

In 1878, Jordan showed that a finite subgroup of GL(n,C) contains an abelian normal subgroup whose index is bounded by a function of n alone. Previously, the author has given precise bounds. Here, we consider analogues for finite linear…

We will prove the following theorems. The first theorem posits the existence of a fixed point for the actions of nilpotent Lie groups on nonpositively curved compact manifolds. The second theorem states that actions of solvable Lie groups…

We prove a number of results linking properties of actions by compact groups (both quantum and classical) on Banach spaces, such as uniform continuity, spectrum finiteness and extensibility of the actions across several constructions.…

We prove that an analogue of Jordan's theorem on finite subgroups of general linear groups holds for the groups of biregular automorphisms of algebraic surfaces. This gives a positive answer to a question of Vladimir L. Popov.

We give a criterion for group elements to have fixed points with respect to a semi-simple action on a complete CAT(0) space of finite topological dimension. As an application, we show that Thompson's group T and various generalizations of…

A group $G$ is said to have property (PH') if there exist finitely many hyperbolic spaces $X_1,\cdots,X_n$ on which $G$ acts coboundedly such that the diagonal action of $G$ on the product $\prod_{i=1}^nX_i$ equipped with $\ell^1$-metric is…

Let $A$ and $B$ be associative algebras over a field $F$ with {\rm char}$(F)\ne 2$. Our first main result states that if $A$ is unital and equal to its commutator ideal, then every Jordan epimorphism $\varphi:A\to B$ is the sum of a…

Given a 4-manifold with a homologically trivial and locally-linear cyclic group action, we obtain necessary and sufficient conditions for the existence of equivariant bundles. The conditions are derived from the twisted signature formula…

The main result of this paper is that all affine isometric actions of higher rank Steinberg groups over commutative rings on uniformly convex Banach spaces have a fixed point. We consider Steinberg groups over classical root systems and our…

Every homomorphism from finite index subgroups of a universal lattices to mapping class groups of orientable surfaces (possibly with punctures), or to outer automorphism groups of finitely generated nonabelian free groups must have finite…

Let $G$ be a bounded simply connected domain in the complex plane. A point $a\in \partial G$ is said to be accessible from inside of $G$ if there is a Jordan arc $J$ such that $J\subset \bar G$ and $J\cap\partial G=\{a\}$. In this paper the…

We study the automorphisms group action on a bounded domain in $\CC^n$ having a boundary point that is exponentially flat. Such a domain typically has a compact automorphism group. Our results enable us to generate many new examples.

We prove that if a geodesically complete $\mathrm{CAT}(0)$ space $X$ admits a proper cocompact isometric action of a group, then the Izeki-Nayatani invariant of $X$ is less than $1$. Let $G$ be a finite connected graph, $\mu_1 (G)$ be the…

We consider self-similar continua possessing finite intersection property and prove intersection graph criterion for self-similar dendrites, finite order Theorem for such continua satisfying open set condition in $\mathbb{R}^n$ and…

The standard actions of finite groups on spheres S^d are linear actions, i.e. by finite subgroups of the orthogonal group O(d+1). We prove that, in each dimension d>5, there is a finite group G which admits a faithful, topological action on…

We provide a unified proof of all known examples of locally compact groups that enjoy the Howe-Moore property, namely, the vanishing at infinity of all matrix coefficients of the group unitary representations that are without non-zero…

We generalize the fixed-point property for discrete groups acting on convex cones given by Monod in \cite{monod} to topological groups. At first, we focus on describing this fixed-point property from a functional point of view, and then we…