arXiv research

The study bounds curve sizes on surfaces using group cubulations.

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 $\mathbf R$-tree $X$ then for any $ε>0$ there is a finite subtree $Y_ε\subseteq X$…

The paper studies acylindrical actions on trees and proves acylindrical hyperbolicity of Baumslag-Solitar groups.

New groups defined that act on trees without repeating.

Proves WPD elements are exponentially generic in acylindrically hyperbolic groups.

Automorphism groups of infinitely-ended groups are acylindrically hyperbolic.

Study shows Morse elements are common in acylindrically hyperbolic groups.

Simplified projection complexes for acylindrical actions proved.

We give a criterion to prove that some groups are not acylindrically hyperbolic. As an application, we prove that the mapping class group of an infinite type surface is not acylindrically hyperbolic.

The study shows acylindrical hyperbolicity for Artin groups not associated with joins or cones.

The Farrell-Jones Conjecture holds for groups acting acylindrically on trees.

New group $Q$ has unusual properties like no uniform non-amenability.

Infinite verbal width for certain groups like hyperbolic and mapping class groups.

Study projection in acylindrically hyperbolic groups, proving sublinear tracking and growth bounds.

Random quotients preserve hyperbolic properties in groups.

We prove that every finitely presented group with positive first $\ell^2$-Betti number that virtually surjects onto $\mathbb Z$ is acylindrically hyperbolic. In particular, this implies acylindrical hyperbolicity of finitely presented residually finite groups with positive first $\ell^2$-Betti number as well as groups …

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, 3-manifold groups and graph products. Acylindrical hyperbolicity is then used to obtain …

Acylindrical hyperbolicity proven for a specific group of automorphisms.

The class of acylindrically hyperbolic groups, which are groups that admit a certain type of non-elementary action on a hyperbolic space, contains many interesting groups such as non-exceptional mapping class groups and $\operatorname{Out}(\mathbb F_n)$ for $n\geq 2$. In such a group, a generalized loxodromic element i…

Artin groups not free of infinity are shown to have finite centers.

Percolation study in non-hyperbolic groups proves non-uniqueness phase.

New largest acylindrical actions found for hierarchically hyperbolic groups.

Study abelian subgroups in 3-manifolds, linking to splitting properties.

Study shows infinite dimensional zero norm subspace in bounded cohomology of acylindrically hyperbolic groups.

An exotic plane exists in an acylindrical 3-manifold without being closed.

Formula found for skinning map contraction in hyperbolic geometry.

Survey of recent Kleinian representation convergence results.

Random subgroups of hyperbolic groups often form free groups and are hyperbolically embedded.

We prove that the outer automorphism group $Out(G)$ is residually finite when the group $G$ is virtually compact special (in the sense of Haglund and Wise) or when $G$ is isomorphic to the fundamental group of some compact $3$-manifold. To prove these results we characterize commensurating endomorphisms of acylindrical…

Random walks on hyperbolic spaces show linear progress with exponential decay.

Extra large Artin groups are simple and have unique geodesics.

The aim of this note is to give the simplest possible proof that Mapping Class Groups of closed hyperbolic surfaces are acylindrically hyperbolic, and more specifically that their curve graphs are hyperbolic and that pseudo-Anosovs act on them as loxodromic WPDs.

Explicit bounds on group size for certain geometric actions.

The study proves conjecture for specific Artin groups.

The paper proves properties of geodesic planes in a specific type of 3-manifold.

Characterizes contracting isometries in CAT(0) cube complexes and acylindrical hyperbolicity of diagram groups.

Improved bounds on acylindricity for right-angled Artin groups.

We consider closed acylindrical surfaces in 3-manifolds and in knot and link complements, and show that the genus of these surfaces is bounded linearly by the number of tetrahedra in the triangulation of the manifold and by the number of rational (or alternating) tangles in a projection of a link (or knot). For each g …

The study shows rigidity properties are lost in hyperbolic generalizations.

Study on Cheeger constant in specific hyperbolic 3-manifolds.

Bound skinning map diameter on hyperbolic 3-manifold rays.

Groups without non-trivial finite normal subgroups have a strong ping pong property.

Study shows $L^{2}$-Betti numbers vanish for certain matrix groups over rings, proving non-acylindrical hyperbolicity.

Cohomology defines hyperbolic spaces and their subgraphs.

We prove that every homomorphism from the elementary Chevalley group over a finitely generated unital commutative ring associated with reduced irreducible classical root system of rank at least 2, and ME analogues of such groups, into acylindrically hyperbolic groups has an absolutely elliptic image. This result provid…

Geodesic planes in 3-manifolds are either closed or dense.

Paper defines a partial order on multibranched surfaces in 3-manifolds.

Regular languages describe contracting geodesics in groups.