Related papers: Classification of joinings for Kleinian groups

Given a group automorphism $\phi:\Gamma\to \Gamma$, one has an action of $\Gamma$ on itself by $\phi$-twisted conjugacy, namely, $g.x=gx\phi(g^{-1})$. The orbits of this action are called $\phi$-conjugacy classes. One says that $\Gamma$ has…

We study lattice embeddings for the class of countable groups $\Gamma$ defined by the property that the largest amenable uniformly recurrent subgroup $A_\Gamma$ is continuous. When $A_\Gamma$ comes from an extremely proximal action and the…

Classical Kleinian groups are discrete subgroups of isometries of H n. The well-known theory of Kleinian groups starts with the definition of their associated limit set in the boundary of H n , and includes the geometric properties of the…

If $n \geq 3$ and $\Gamma$ is a convex-cocompact Zariski-dense discrete subgroup of $\mathbf{SO}^o(1,n+1)$ such that $\delta_\Gamma=n-m$ where $m$ is an integer, $1 \leq m \leq n-1$, we show that for any $m$-dimensional subgroup $U$ in the…

We give a geometric characterization of finite rational groups. In particular, we prove that a finite group is rational if and only if there exists a finite geometry $\Gamma$ of type $I$ and action of $G$ on $\Gamma$ as a group of…

Given a fixed integer n, we consider closed subgroups G of H = GL(n,Z_p) where Z_p denotes the ring of p-adic integers and p is sufficiently large in terms of n. Assuming that the Zariski closure of G has no toric part, we give a condition…

The dense amalgam is an operation (introduced in arXiv:1410.4989) which to any finite collection of metrizable compacta associates canonically some new highly disconnected compact metrisable space in which embedded copies of the initial…

The end compactification |\Gamma| of the locally finite graph \Gamma is the union of the graph and its ends, endowed with a suitable topology. We show that \pi_1(|\Gamma|) embeds into a nonstandard free group with hyperfinitely many…

The Sylow graph $\Gamma(G)$ of a finite group $G$ originated from recent investigations on the so--called $\mathbf{N}$--closed classes of groups. The connectivity of $\Gamma(G)$ was proved only few years ago, involving the classification of…

In 2012 the second author obtained a description of the lattice of subgroupsof a Chevalley group $G(\Phi,A)$, containing the elementary subgroup $E(\Phi,K)$ over a subring $K\subseteq A$ provided $\Phi=B_n,$ $C_n$ or $F_4$, $n\ge2$, and $2$…

Let p be a rational prime, k be a perfect field of characteristic p and K be a finite totally ramified extension of the fraction field of the Witt ring of k. Let G be a finite flat commutative group scheme over O_K killed by some p-power.…

Let $\calM=\Gamma\bs \calH^{(n)}$, where $\calH^{(n)}$ is a product of $n+1$ hyperbolic planes and $\Gamma\subset\PSL(2,\bbR)^{n+1}$ is an irreducible cocompact lattice. We consider closed geodesics on $\calM$ that propagate locally only in…

We begin by showing that commensurators of Zariski dense subgroups of isometry groups of symmetric spaces of non-compact type are discrete provided that the limit set on the Furstenberg boundary is not invariant under the action of a…

We show that if $\Gamma$ is a co-compact arithmetic lattice in $SL(2,\mathbb{R})$ or $\Gamma=SL(2,\mathbb{Z})$ then the horocycle orbit of every non-periodic point $x\in SL(2,\mathbb{R})/\Gamma$ equidistributes (with respect to Haar…

It is well-known that an element of the linear group ${\rm GL}_n(\C)$ is semisimple if and only if its conjugacy class is Zariski closed. The aim of this paper is to show that the same result holds for the group of complex plane polynomial…

Let $G$ be a group. Two elements $x, y$ are said to be {\it $z$-equivalent} if their centralizers are conjugate in $G$. The class equation of $G$ is the partition of $G$ into conjugacy classes. Further decomposition of conjugacy classes…

We propose a new method for studying $n$- and $\Gamma$-cohomology of globalizations of Harish-Chandra modules, where $G=KAN$ is a rank one semisimple Lie group, $\Gamma$ is a discrete subgroup of $G$ and $n=Lie(N)$. We prove a conjecture of…

Let $G$ and $\tilde G$ be Kleinian groups whose limit sets $S$ and $\tilde S$, respectively, are homeomorphic to the standard Sierpi\'nski carpet, and such that every complementary component of each of $S$ and $\tilde S$ is a round disc. We…

Let $\Gamma$ be a finitely generated group, and let $\mu$ be a nondegenerate, finitely supported probability measure on $\Gamma$. We show that every co-compact $\Gamma$ action on a locally compact Hausdorff space admits a nonzero…

Let G be a connected semisimple Lie group with finite center and without compact factors, P a minimal parabolic subgroup of G, and \Gamma a lattice in G. We prove that every \Gamma-orbits in the Furstenberg boundary G/P is equidistributed…