Related papers: Semigroup Actions, Covering Spaces and Schutzenber…

We study groups acting by length-preserving transformations on spaces equipped with asymmetric, partially-defined distance functions. We introduce a natural notion of quasi-isometry for such spaces and exhibit an extension of the…

We detect topological semigroups that are topological paragroups, i.e., are isomorphic to a Rees product of a topological group over topological spaces with a continuous sandwich function. We prove that a simple topological semigroup $S$ is…

We extend the definition of Weinstein's Action homomorphism to Hamiltonian actions with equivariant moment maps of (possibly infinite-dimensional) Lie groups on symplectic manifolds, and show that under conditions including a uniform bound…

The present work investigates regular, semiregular, and chiral polytopes of any rank $d\geq 3$, whose automorphism groups are 2-groups. There is a large variety of rather small finite regular or alternating semiregular polytopes with…

We study actions of discrete groups on 2-categories. The motivating examples are actions on the 2-category of representations of finite tensor categories and their relation with the extension theory of tensor categories by groups.…

Let $G$ be a group acting properly by isometries and with a strongly contracting element on a geodesic metric space. Let $N$ be an infinite normal subgroup of $G$, and let $\delta_N$ and $\delta_G$ be the growth rates of $N$ and $G$ with…

We consider the pseudo-Riemannian Lichnerowicz conjecture in the homogeneous setting. In particular, we show that any compact connected pseudo-Riemannian manifold $M$ on which a semisimple group $G$ acts conformally, essentially and…

We characterise connected cubic graphs admitting a vertex- transitive group of automorphisms with an abelian normal subgroup that is not semiregular. We illustrate the utility of this result by using it to prove that the order of a…

It is known that the canonical double cover of any connected nonbipartite graph have an automorphism group of the form $H \rtimes \mathbb{Z}_2$, where $H$ is the set of automorphism which preserve bipartite parts. We construct connected…

We consider pairs (V,H) of subgroups of a connected unipotent complex Lie group G for which the induced VxH-action on G by multiplication from the left and from the right is free. We prove that this action is proper if the Lie algebra g of…

We show that a continuous action of a quantum semigroup $\mathcal{S}$ on a finite quantum space (finite dimensional $\mathrm{C}^*$-algebra) preserving a faithful state comes from a continuous action of the quantum Bohr compactification…

We study equicontinuous actions of semisimple groups and some generalizations. We prove that any such action is universally closed, and in particular proper. We derive various applications, both old and new, including closedness of…

Let $G$ be a countable group with no finitely generated subgroup of exponential growth. We show that every action of $G$ on a countable set preserving a linear (respectively, circular) order can be realised as the restriction of some action…

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…

We consider a version of the notion of F-inverse semigroup (studied in the algebraic theory of inverse semigroups). We point out that an action of such an inverse semigroup on a locally compact space has associated a natural groupoid…

Given a Baumslag-Solitar group, we study its space of subgroups from a topological and dynamical perspective. We first determine its perfect kernel (the largest closed subset without isolated points). We then bring to light a natural…

The superextension $\lambda(X)$ of a set $X$ consists of all maximal linked families on $X$. Any associative binary operation $*: X\times X \to X$ can be extended to an associative binary operation $*:…

Let $(X,G)$ be a minimal equicontinuous dynamical system, where $X$ is a compact metric space and $G$ some topological group acting on $X$. Under very mild assumptions, we show that the class of regular almost automorphic extensions of…

We define and develop the notion of a discretisable quasi-action. It is shown that a cobounded quasi-action on a proper non-elementary hyperbolic space $X$ not fixing a point of $\partial X$ is quasi-conjugate to an isometric action on…

This study delves into the exploration of the limiting shape theorem for subadditive processes on finitely generated groups with polynomial growth, commonly referred to as virtually nilpotent groups. Investigating the algebraic structures…