Results 31 to 40 of about 45 (45)

Tree-like graphings, wallings, and median graphings of equivalence relations

Forum of Mathematics, Sigma
We prove several results showing that every locally finite Borel graph whose large-scale geometry is ‘tree-like’ induces a treeable equivalence relation.
Ruiyuan Chen, Antoine Poulin, Ran Tao, Anush Tserunyan   +3 more
doaj   +1 more source

Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups

Analysis and Geometry in Metric Spaces
We show that infinite cyclic subgroups of groups acting uniformly properly on injective metric spaces are uniformly undistorted. In the special case of hierarchically hyperbolic groups, we use this to study translation lengths for actions on the ...
Abbott Carolyn, Hagen Mark, Petyt Harry, Zalloum Abdul   +3 more
doaj   +1 more source

Hyperfiniteness of boundary actions of acylindrically hyperbolic groups

Forum of Mathematics, Sigma
We prove that, for any countable acylindrically hyperbolic group G, there exists a generating set S of G such that the corresponding Cayley graph $\Gamma (G,S)$ is hyperbolic, $|\partial \Gamma (G,S)|>2$ , the natural action of G on ...
Koichi Oyakawa
doaj   +1 more source

Rigidity phenomena and the statistical properties of group actions on $\text {CAT}(0)$ cube complexes

Forum of Mathematics, Sigma
We compare the marked length spectra of some pairs of proper and cocompact cubical actions of a nonvirtually cyclic group on $\mathrm {CAT}(0)$ cube complexes.
Stephen Cantrell, Eduardo Reyes
doaj   +1 more source

Thompson’s group T has quadratic Dehn function

Forum of Mathematics, Sigma
We prove that Thompson’s group T and, more generally, all the Higman–Thompson groups $T_n$ have quadratic Dehn function.
Matteo Migliorini
doaj   +1 more source

Limit trees for free group automorphisms: universality

Forum of Mathematics, Sigma
To any free group automorphism, we associate a universal (cone of) limit tree(s) with three defining properties: first, the tree has a minimal isometric action of the free group with trivial arc stabilizers; second, there is a unique expanding dilation ...
Jean Pierre Mutanguha
doaj   +1 more source

Posets arising from decompositions of objects in a monoidal category

Forum of Mathematics, Sigma
Given a symmetric monoidal category ${\mathcal C}$ with product $\sqcup $ , where the neutral element for the product is an initial object, we consider the poset of $\sqcup $ -complemented subobjects of a given object X.
Kevin Ivan Piterman, Volkmar Welker
doaj   +1 more source

Group Approximation in Cayley Topology and Coarse Geometry, Part II: Fibred Coarse Embeddings

Analysis and Geometry in Metric Spaces, 2019
The objective of this series is to study metric geometric properties of disjoint unions of Cayley graphs of amenable groups by group properties of the Cayley accumulation points in the space of marked groups.
Mimura Masato, Sako Hiroki
doaj   +1 more source

Geometry of Generated Groups with Metrics Induced by Their Cayley Color Graphs

Analysis and Geometry in Metric Spaces, 2019
Let G be a group and let S be a generating set of G. In this article,we introduce a metric dC on G with respect to S, called the cardinal metric.We then compare geometric structures of (G, dC) and (G, dW), where dW denotes the word metric. In particular,
Suksumran Teerapong
doaj   +1 more source

The conjugacy problem for $\operatorname {Out}(F_3)$

Forum of Mathematics, Sigma
We present a solution to the conjugacy problem in the group of outer automorphisms of $F_3$ , a free group of rank 3. We distinguish according to several computable invariants, such as irreducibility, subgroups of polynomial growth and subgroups ...
François Dahmani, Stefano Francaviglia, Armando Martino, Nicholas Touikan   +3 more
doaj   +1 more source