Related papers: Accessibility of partially acylindrical actions

We prove an acylindrical accessibility theorem for finitely generated groups acting on $\mathbf R$-trees. Namely, we show that if $G$ is a freely indecomposable non-cyclic $k$-generated group acting minimally and $M$-acylindrically on an…

We find a condition on the acylindrical action of a finitely presented group on a simplicial tree which guarantees that this action will be dominated by an acylindrical action with finitely generated edge stabilisers, and find the first…

We identify natural conditions for a countable group acting on a countable tree which imply that the orbit equivalence relation of the induced action on the Gromov boundary is Borel hyperfinite. Examples of this condition include…

This paper explores acylindrical actions on trees, building on previous works related to the mapping class group and projection complexes. We demonstrate that the quotient action of a $1$-acylindrical action of a group on a tree by an…

We bound the size of $d$-dimensional cubulations of finitely presented groups. We apply this bound to obtain acylindrical accessibility for actions on CAT(0) cube complexes and bounds on curves on surfaces.

We prove that there exists a positive, explicit function $F(k, E)$ such that, for any group $G$ admitting a $k$-acylindrical splitting and any generating set $S$ of $G$ with $\mathrm{Ent}(G,S)<E$, we have $|S| \leq F(k, E)$. We deduce…

Let $G$ be a connected reductive group over a perfect field $k$ acting on an algebraic variety $X$ and let $P$ be a minimal parabolic subgroup of $G$. For $k$-spherical $G$-varieties we prove finiteness result for $P$-orbits that contain…

We construct affine uniformly Lipschitz actions on $\ell^1$ and $L^1$ for certain groups with hyperbolic features. For acylindrically hyperbolic groups, our actions have unbounded orbits, while for residually finite hyperbolic groups and…

We develop a notion of groups that act acylindrically and non-elementarily on simplicial trees, which we call acylindrically arboreal groups. We then prove a complete classification of when graph products of groups and the fundamental…

It is shown that the restriction of the action of any group with finite orbit on the minimal sets of dendrites is equicontinuous. Consequently, we obtain that the action of any amenable group and Thompson group on dendrite restricted on…

For group actions on hyperbolic CAT(0) square complexes, we show that the acylindricity of the action is equivalent to a weaker form of acylindricity phrased purely in terms of stabilisers of points, which has the advantage of being much…

We provide new examples of acylindrically hyperbolic groups arising from actions on simplicial trees. In particular, we consider amalgamated products and HNN-extensions, 1-relator groups, automorphism groups of polynomial algebras,…

We investigate a family of groups acting on a regular tree, defined by prescribing the local action almost everywhere. We study lattices in these groups and give examples of compactly generated simple groups of finite asymptotic dimension…

In this paper we consider the finite groups that act fiber- and orientation-preservingly on closed, compact, and orientable Seifert manifolds that fiber over an orientable base space. We establish a method of constructing such group actions…

In this paper we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group $G$ on a manifold $X$, these results provide information on the restriction of the action to a subgroup of…

In this note we derive an upper bound on the number of 2-spheres in the fixed point set of a smooth and homologically trivial cyclic group action of prime order on a simply-connected 4-manifold. This improves the a priori bound which is…

The reality of the difficulties in investigation of finite groups are considered. It is shown that the consideration of symmetry properties of the $k$-orbits that are obtained with an action of a finite group $F=(V,\cdot)$ on Cartesian…

We give necessary and sufficient conditions under which a quasi-action of any group on an arbitrary metric space can be reduced to a cobounded isometric action on some bounded valence tree, following a result of Mosher, Sageev and Whyte.…

We derive a lower and an upper bound for the rank of the finite part of operator $K$-theory groups of maximal and reduced $C^*$-algebras of finitely generated groups. The lower bound is based on the amount of polynomially growing conjugacy…

This is the first paper in a series of three where we take on the unified theory of non-Archimedean group actions, length functions and infinite words. Our main goal is to show that group actions on Z^n-trees give one a powerful tool to…