Related papers: On {\Gamma}-embeddings and partial actions of func…

In this paper, we have proved results similar to Tychonoff's Theorem on embedding a space of functions with the topology of pointwise convergence into the Tychonoff product of topological spaces, but applied to the function space $C(X,Y)$…

The first part of the paper centers in the study of embeddability between partially commutative groups. In [KK], for a finite simplicial graph $\Gamma$, the authors introduce an infinite, locally infinite graph $\Gamma^e$, called the…

Let $\Gamma$ be a finitely generated group which admits an action by homeomorphisms on a compact metrizable space $X$. We show that there is a metric on $X$ defining the original topology such that for this metric, the action is by…

Let a group $\Gamma$ act on a paracompact, locally compact, Hausdorff space $M$ by homeomorphisms and let $2^M$ denote the set of closed subsets of $M$. We endow $2^M$ with the Chabauty topology, which is compact and admits a natural…

In this article, we introduce the concept of partial actions of a group $G$ on quivers and demonstrate that for any given partial action of G on a quiver $\Gamma$, there exists another quiver, $\Gamma'$ with a full $G$-action. This is an…

We analyse the structure of the quotient $\mathrm{A}_\sim(\Gamma,X,\mu)$ of the space of measure-preserving actions of a countable discrete group by the relation of weak equivalence. This space carries a natural operation of convex…

We prove an equivariant version of the classical Menger-Nobeling theorem regarding topological embeddings: Whenever a group $G$ acts on a finite-dimensional compact metric space $X$, a generic continuous equivariant function from $X$ into…

We generalize Exel's notion of partial group action to monoids. For partial monoid actions that can be defined by means of suitably well-behaved systems of generators and relations, we employ classical rewriting theory in order to describe…

The topological symmetry group $\mathrm{TSG}(\Gamma)$ of an embedding $\Gamma$ of a graph in $S^3$ is the subgroup of the automorphism group of the graph which is induced by homeomorphisms of $(S^3,\Gamma)$. If we restrict to orientation…

We have defined and established a theory of cofinite connectedness of a cofinite graph. Many of the properties of connectedness of topological spaces have analogs for cofinite connectedness. We have seen that if $G$ is a cofinite group and…

In this paper, we find at the properties of the family lambda which imply that the function space C(X,R^alpha) with the lambda-open topology is a semitopological group (paratopological group, topological group, topological vector space and…

We develop a class of homeomorphisms on a compact homogeneous space of a transitive group action and show how the class sheds new light on a decomposition problem. We further use this class to show that every such homogeneous space in a…

We introduce a topology on the space of actions modulo weak equivalence finer than the one previously studied in the literature. We show that the product of actions is a continuous operation with respect to this topology, so that the space…

Let M be a Riemann surface with boundary $\partial M$ and genus greater than zero. Let $\Gamma$ be the mapping class group of M fixing $\partial M$. The group $\Gamma$ acts on ${\mathcal M}_{\mathcal C} = \Hom_{\mathcal…

Let $\Gamma$ be a finitely generated group and $X$ be a minimal compact $\Gamma$-space. We assume that the $\Gamma$-action is micro-supported, i.e. for every non-empty open subset $U \subseteq X$, there is an element of $\Gamma$ acting…

Rubin's theorem asserts that if $\Gamma\curvearrowright X$ and $\Delta\curvearrowright Y$ are Rubin actions, then any group isomorphism $\Gamma \cong \Delta$ induces an equivariant homeomorphism $Y\cong X$. We provide an embedding version…

We present a simple approach to questions of topological orbit equivalence for actions of countable groups on topological and smooth manifolds. For example, for any action of a countable group $\Gamma$ on a topological manifold where the…

We consider the moduli space ${\cal M}(G)$ of $G$-Higgs bundles over a compact Riemann surface $X$, where $G$ is a semisimple complex Lie group, and study the action of a finite group $\Gamma$ on ${\cal M}(G)$ induced by a holomorphic…

In this two part work we prove that for every finitely generated subgroup $\Gamma < \text{Out}(F_n)$, either $\Gamma$ is virtually abelian or $H^2_b(\Gamma;\mathbb{R})$ contains an embedding of $\ell^1$. The method uses actions on…

For a cardinal $\kappa$, denote by $\mathbf{H}^\kappa$ the algebraic real hyperbolic space of dimension $\kappa$. For a topological group $\Gamma$, we study the set of continuous representations $\Gamma \to…