Related papers: On groups whose actions on finite-dimensional CAT(…

We show that any action of a finite group on a finitely presentable group arises as the action of the group of self-homotopy equivalences of a space on its fundamental group. In doing so, we prove that any finite connected (abstract)…

In this article, we prove the existence of common fixed points for a pair of maps on a $q$-spherically complete $T_0$-ultra-quasi-metric space. The present article is a generalization, in the assymmetric setting of the paper of Rao et…

We study the fixed point set in the ideal boundary of a parabolic isometry of a proper CAT(0)-space. We show that the radius of the fixed point set is at most pi/2, and study its centers. As a consequence, we prove that the set of fixed…

Let G be a one-ended group acting discretely and co-compactly on a CAT(0) space X. We show that the boundary of X has no cut points and that one can detect splittings of $G$ over two-ended groups and recover its JSJ decomposition from the…

We prove that for each integer k of at least 2, there is an open neigborhood \nu_k of the identity map of the 2-sphere S^2, in C^1-topology such that: if G is a nilpotent subgroup of Diff^1(S^2) with length k of nilpotency, generated by…

We show that every real analytic action of a connected supersoluble Lie group on a compact surface with nonzero Euler characteristic has a fixed point. This implies that E. Lima's fixed point free $C^{\infty}$ action on $S^2$ of the affine…

We investigate some properties of the clopen type semigroup of an action of a countable group on a compact, $0$-dimensional, Hausdorff space X. We discuss some characterizations of dynamical comparison (most of which were already known in…

The goal of this paper is proving the existence and then localizing global fixed points for nilpotent groups generated by homeomorphisms of the plane satisfying a certain Lipschitz condition. The condition is inspired in a classical result…

The aim of this note is to give simple proofs of some results of Reichstein and Youssin (math.AG/9903162) about the behaviour of fixed points of finite group actions under rational maps. Our proofs work in any characteristic. We also give a…

Does every one-ended $CAT(0)$ group have semistable fundamental group at infinity? As we write, this is an open question. Let $G$ be such a group acting geometrically on the proper $CAT(0)$ space $X$. In this paper we show that in order to…

If $X$ is a smooth manifold and ${\mathcal{G}}$ is a subgroup of $Diff(X)$ we say that $(X,{\mathcal{G}})$ has the almost fixed point property if there exists a number $C$ such that for any finite subgroup $G\leq{\mathcal{G}}$ there is some…

In this paper, we study almost finiteness and almost finiteness in measure of non-free actions. Let $\alpha:G\curvearrowright X$ be a minimal action of a locally finite-by-virtually $\mathbb{Z}$ group $G$ on the Cantor set $X$. We prove…

It is a consequence of the classical Jordan bound for finite subgroups of linear groups that in each dimension n there are only finitely many finite simple groups which admit a faithful, linear action on the n-sphere. In the present paper…

Hughes has defined a class of groups, which we call FSS (finite similarity structure) groups. Each FSS group acts on a compact ultrametric space by local similarities. The best-known example is Thompson's group V. Guided by previous work on…

In this paper, we discuss the fixed point property for an infinite family of order-preserving mappings which satisfy the Lipschitzian condition on comparable pairs. The underlying framework of our main results is a metric space of any…

The iterated monodromy group of a post-critically finite complex polynomial of degree d \geq 2 acts naturally on the complete d-ary rooted tree T of preimages of a generic point. This group, as well as its pro-finite completion, act on the…

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…

A seminal result in geometric group theory is that a 1-ended hyperbolic group has a locally connected visual boundary. As a consequence, a 1-ended hyperbolic group also has a path connected visual boundary. In this paper, we study when this…

We investigate fixed point properties for isometric actions of topological groups on a wide class of metric spaces, with a particular emphasis on Hilbert spaces. Instead of requiring the action to be continuous, we assume that it is…

Given an action by a finite quantum group $\mathbb{G}$ on a von Neumann algebra $M$, we prove that a number of familiar $W^*$ properties are equivalent for $M$ and the fixed-point algebra $M^{\mathbb{G}}$ (i.e. hold or not simultaneously…