Related papers: Group actions on geodesic Ptolemy spaces

We prove that if X is a complete geodesic metric space with uniformly generated first homology group and $f: X\to R$ is metrically proper on the connected components and bornologous, then X is quasi-isometric to a tree. Using this and…

We study properly discontinuous and cocompact actions of a discrete subgroup $\Gamma$ of an algebraic group $G$ on a contractible algebraic manifold $X$. We suppose that this action comes from an algebraic action of $G$ on $X$ such that a…

We study cohomogeneity one Riemannian manifolds and we establish some simple criterium to test when a singular orbit is totally geodesic. As an application, we classify compact, positively curved Riemannian manifolds which are acted on…

Compact hyperbolic 3-manifolds are used in cosmological models. Their topology is characterized by their homotopy group $\pi_1(M)$ whose elements multiply by path concatenation. The universal covering of the compact manifold $M$ is the…

Let G be a group and let M be a CAT(0) proper metric space (e.g. a simply connected complete Riemannian manifold of non-positive sectional curvature or a locally finite tree). Isometric actions of G on M are (by definition) points in the…

Let X be a proper hyperbolic geodesic metric space and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G is not amenable then its second continuous bounded cohomology group with coefficients the regular…

We prove a Morse Lemma for coarsely regular quasigeodesics in nonpositively curved symmetric spaces and euclidean buildings X. The main application is a simpler coarse geometric characterization of Morse subgroups of the isometry groups…

A $\mathbb{C}^{*}$-action on a projective variety $X$ is said to be of Euler type at a nonsingular fixed point $x$ if the isotropy action of $\mathbb{C}^{*}$ on $T_{x}X$ is by scalar multiplication. In this paper, it's proven that a smooth…

We propose a notion of isometric coaction of a compact quantum group on a compact quantum metric space in the framework of Rieffel where the metric structure is given by a Lipnorm. We prove the existence of a quantum isometry group for…

An isometric action of a Lie group on a Riemannian manifold is of cohomogeneity one if the corresponding orbit space is one-dimensional. In this article we develop a conceptual approach to the classification of cohomogeneity one actions on…

We prove a quantitative version of the classical Tits' alternative for discrete groups acting on packed Gromov-hyperbolic spaces supporting a convex geodesic bicombing. Some geometric consequences, as uniform estimates on systole, diastole,…

In this monograph we lay the foundation for a theory of coarse groups and coarse actions. Coarse groups are group objects in the category of coarse spaces, and can be thought of as sets with operations that satisfy the group axioms "up to…

Two groups are virtually isomorphic if they can be obtained one from the other via a finite number of steps, where each step consists in taking a finite extension or a finite index subgroup (or viceversa). Virtually isomorphic groups are…

Let $\varphi$ and $\varphi'$ be two homotopic actions of the topological group $G$ on the topological space $X$. To an object $A$ in the $G$-equivariant derived category $D_{\varphi}(X)$ of $X$ relative to the action $\varphi$ we associate…

We classify compact homogeneous geometries of irreducible spherical type and rank at least 2 which admit a transitive action of a compact connected group, up to equivariant 2-coverings. We apply our classification to polar actions on…

We classify representations of compact connected Lie groups whose induced action on the unit sphere has an orbit space isometric to a Riemannian orbifold.

We study isometric actions on Riemannian symmetric spaces of noncompact type which are induced by reductive algebraic subgroups of the isometry group. We show that for such an action there exists a corresponding isometric action on a dual…

Starting from the classical results of Shubnikov and Zamorzayev, computer models of shapes are implemented, which allow to visualize the action of discrete subgroups of continuous topological groups. The action is visualize by performing…

A proper isometric Lie group action on a Riemannian manifold is called polar if there exists a closed connected submanifold which meets all orbits orthogonally. In this article we study polar actions on Damek-Ricci spaces. We prove criteria…

Let a discrete group $G$ possess two convergence actions by homeomorphisms on compacta $X$ and $Y$. Consider the following question: does there exist a convergence action $G{\curvearrowright}Z$ on a compactum $Z$ and continuous equivariant…