Related papers: Limit group invariants for non-free Cantor actions

Quasi-free actions of finite groups on Cuntz algebras $\mathcal O_n$ for $n\geq 2$ are classified up to conjugacy by data in the representation ring. Partial results are obtained for quasi-free actions by compact groups.

Let $G$ be a non-elementary word-hyperbolic group acting as a convergence group on a compact metrizable space $Z$ so that there exists a continuous $G$-equivariant map $i:\partial G\to Z$, which we call a \emph{Cannon-Thurston map}. We…

Actions of finite groups on stable curves are studied. They appear naturally at the boundary of a moduli space of smooth curves with group actions. Those actions which can equivariantly smoothed are characterised. A description of…

We show that the group of homeomorphisms of the Cantor set $H(K)$ has ample generics, that is, for every $m$ the diagonal conjugacy action $g\cdot(h_1,h_2,..., h_m)=(gh_1g^{-1},gh_2g^{-1},..., gh_mg^{-1})$ of $H(K)$ on $H(K)^m$ has a…

We initiate an investigation into the local structure of simple nonnuclear C$^*$-crossed products by showing that stable rank one is generic within two natural classes of minimal actions of free groups on the Cantor set. The arguments also…

In this paper we study actions of finite groups on closed connected aspherical manifolds. Under some assumptions on the outer automorphism group of the fundamental group of a closed connected aspherical manifold $M$, we prove that the…

Consider homogeneous G/H and G/F, for an S-algebraic group G. A lattice {\Gamma} acts on the left strictly conservatively. The following rigidity results are obtained: morphisms, factors and joinings defined apriori only in the measurable…

Consider a lattice $\Gamma$ in a group $G = SL_2(\R), SO(1,n), SU(1,n)$, $SL_2(\Q_p)$. We discuss actions of $\Gamma$ by affine isometric transformations of Hilbert spaces. We show that for irreducible affine isometric action of $G$ its…

In this paper we study conditions under which a free minimal $\mz^d$-action on the Cantor set is a topological extension of the action of $d$ rotations, either on the product $\mt^d$ of $d$ 1-tori or on a single 1-torus $\mt^1$. We extend…

Let $G$ be a second-countable, locally compact group. In this article we study amenable $G$-actions on Kirchberg algebras that admit an approximately central embedding of a canonical quasi-free action on the Cuntz algebra…

For a locally compact group $G$ we consider the algebra $CD(G)$ of convolution dominated operators on $L^{2}(G)$: An operator $A:L^2(G)\to L^2(G)$ is called convolution dominated if there exists $a\in L^1(G)$ such that for all $f \in…

We study amenability of definable and topological groups. Among our main technical tools is an elaboration on and strengthening of the Massicot-Wagner version of the stabilizer theorem, and some results around measures. As an application we…

The transitivity degree of a group $G$ is the supremum of all integers $k$ such that $G$ admits a faithful $k$-transitive action. Few obstructions are known to impose an upper bound on the transitivity degree for infinite groups. The…

Let $\mathbb{G}$ be a compact Hausdorff group acting on a compact Hausdorff space $X$, $\alpha$ an irreducible $\mathbb{G}$-representation, and $C(X)$ the $C^*$-algebra of complex-valued continuous functions on $X$. We prove that the…

Let $G$ be a compact Lie group. Let ${\mathsf{F}}_n$ be the free group of rank $n$. We describe the orbits of ${\mathsf{Aut}}(\mathsf{F}_n)$ on ${\mathsf{Hom}}(\mathsf{F}_n;G)$ when $n$ is sufficiently large. The dynamics stabilizes: orbit…

In the wake of a preceding article \cite{RogUnt06} introducing the Schr\"odinger-Virasoro group, we study its affine action on a space of $(1+1)$-dimensional Schr\"odinger operators with time- and space-dependent potential $V$ periodic in…

In this paper we study the orbit closure problem for a reductive group $G\subseteq GL(X)$ acting on a finite dimensional vector space $V$ over $\C$. We assume that the center of $GL(X)$ lies within $G$ and acts on $V$ through a fixed…

Let $M^{2d}$ be a compact symplectic manifold and $T$ a compact $n$-dimensional torus. A Hamiltonian action, $\tau$, of $T$ on $M$ is a GKM action if, for every $p \in M^T$, the isotropy representation of $T$ on $T_pM$ has pair-wise…

Suppose that a group $G$ acts non-elementarily on a hyperbolic space $S$ and does not fix any point of $\partial S$. A subgroup $H\le G$ is said to be geometrically dense in $G$ if the limit sets of $H$ and $G$ coincide and $H$ does not fix…

Let $G$ be a locally compact abelian group. By modifying a theorem of Pedersen, it follows that actions of $G$ on $C^*$-algebras $A$ and $B$ are outer conjugate if and only if there is an isomorphism of the crossed products that is…