Related papers: Nilpotent Endomorphisms of Expansive Group Actions

H. Gl\"ockner and G. A. Willis have recently shown that locally pro-p contraction groups are nilpotent. The proof hinges on a fixed-point result: if the local field $\mathbb{F}_{p}(\!(t)\!)$ acts on its $d$-th power…

We prove that a random group of the graph model associated with a sequence of expanders has fixed-point property for a certain class of CAT(0) spaces. We use Gromov's criterion for fixed-point property in terms of the growth of n-step…

We show that for a locally free action of a simply connected nilpotent Lie group on a compact manifold, if every real valued cocycle is cohomologous to a constant cocycle, then the action is parameter rigid. The converse is true if the…

A finitely generated group $\Gamma$ is called strongly scale-invariant if there exists an injective endomorphism $\varphi: \Gamma \to \Gamma$ with the image $\varphi(\Gamma)$ of finite index in $\Gamma$ and the subgroup $\displaystyle…

This self-contained paper is part of a series \cite{FF2,FF3} on actions by diffeomorphisms of infinite groups on compact manifolds. The two main results presented here are: 1) Any homomorphism of (almost any) mapping class group or…

Let $K$ be a field and $f:\mathbb{P}^N \to \mathbb{P}^N$ a morphism. There is a natural conjugation action on the space of such morphisms by elements of the projective linear group $\text{PGL}_{N+1}$. The group of automorphisms, or…

We study isometric actions of Steinberg groups on Hadamard manifolds. We prove some rigidity properties related to these actions. In Particular we show that every isometric action of $St_n(F_p\langle t_1,\ldots ,t_k \rangle)$ on Hadamard…

In this paper we study expansions of infinite dimensional Hilbert spaces with a unitary representation of a discrete countable group. When the group is finite, we prove the theory of the corresponding expansion, regardless if it is…

A virtual endomorphism of a group G is a homomorphism f from H into G where H is a subgroup of G of finite index m. The triple (G,H,f) produces a state-closed (or, self-similar) representation t of G on the 1-rooted m-ary tree. This paper…

In recent work, Stokes and Vermant considered graph-of-groups realisations of hypergraphs as a new description of rigidity-theoretic problems. In this paper, we show that the infinitesimal aspects of graph-of-groups realisations can be…

We introduce the {\it Ellis semigroup} of a nonautonomous discrete dynamical system $(X,f_{1,\infty})$ when $X$ is a metric compact space. The underlying set of this semigroup is the pointwise closure of $\{f\sp{n}_1 \, |\, n\in…

We study the following question: under what conditions extension of one residually nilpotent group by another residually nilpotent group is residually nilpotent? We prove some sufficient conditions under which this extension is residually…

Let $K$ be a compact metrizable group and $\Ga$ be a group of automorphisms of $K$. We first show that each $\ap \in \Ga$ is distal on $K$ implies $\Ga$ itself is distal on $K$, a local to global correspondence provided $\Ga$ is a…

In this thesis I study the automorphism tower of free nilpotent groups. Our main tool in studying the automorphism tower is to embed every group as a lattice in some Lie group. Using known rigidity results the automorphism group of the…

Ray nil-affine geometries are defined on nilpotent spaces. They occur in every parabolic geometry and in those cases, the nilpotent space is an open dense subset of the corresponding flag manifold. We are interested in closed manifolds…

We are dealing with the question whether every group or semigroup action (with some additional property) on a continuum (with some additional property) has a fixed point. One of such results was given in 2009 by Shi and Sun. They proved…

We show that genuinely higher rank expanding actions of abelian semi-groups on compact manifolds are $C^{\infty}$-conjugate to affine actions on infra-nilmanifolds. This is based on the classification of expanding diffeomorphisms up to…

We study the class of groups having the property that every non-nilpotent subgroup is equal to its normalizer. These groups are either soluble or perfect. We completely describe the structure of soluble groups and finite perfect groups with…

We consider the actions of (semi)groups on a locally compact group by automorphisms. We show the equivalence of distality and pointwise distality for the actions of a certain class of groups. We also show that a compactly generated locally…

In this paper we prove the trace formulas for the Reidemeister numbers of group endomorphisms in the following cases:the group is finitely generated and an endomorphism is eventually commutative; the group is finite ; the group is a direct…