Related papers: Further results on monoids acting on trees

We construct p.m.p. group actions that are not local-global limits of sequences of finite graphs. Moreover, they do not weakly contain any sequence of finite labeled graphs. Our methods are based on the study of almost automorphisms of…

Let \Gamma be a geometrically finite tree lattice. We prove a Khintchine-Sullivan type theorem for the Hausdorff measure of the points at infinity of the tree that are well approximated by the parabolic fixed points of G. Using Bruhat-Tits…

We associate a 2-complex to the following data: a presentation of a semigroup $S$ and a transitive action of $S$ on a set $V$ by partial transformations. The automorphism group of the action acts properly discontinuously on this 2-complex.…

In the paper we introduce a notion of the Bruck-Reilly $\lambda$-polycyclic extension of a monoid $S$ with a homomorphism $\theta$ which is an analogue of the Bruck-Reilly extension of a monoid $S$. We describe idempotens of the semigroup…

We study the positive theory of groups acting on trees and show that under the presence of weak small cancellation elements, the positive theory of the group is trivial, i.e. coincides with the positive theory of a non-abelian free group.…

We propose a novel approach for studying rooted trees by using functions that we will call descent functions. We provide a construction method for rooted trees that allows to study their properties through the use of descent functions.…

We introduce the concept of an extension of a semilattice of groups $A$ by a group $G$ and describe all the extensions of this type which are equivalent to the crossed products $A*_\Theta G$ by twisted partial actions $\Theta$ of $G$ on…

Semigroup actions and their invertible extensions are discussed. First, we develop a theory of natural extensions for continuous actions of countable, embeddable semigroups. Second, we demonstrate that not every surjective such action of a…

We show that every connected graph $G$ has a tree decomposition indexed by a tree $T$ such that $T$ is a subgraph of $G$ and the width of the tree decomposition is bounded from above by a function of the pathwidth of $G$. This answers a…

Motivated by some alternatives to the classical logical model of boolean algebra, this paper deals with algebraic structures which extend skew lattices by locally invertible elements. Following the meme of the Ehresmann-Schein-Nambooripad…

We prove that there are groups in the constructible universe whose automorphism towers are highly malleable by forcing. This is a consequence of the fact that, under a suitable diamond hypothesis, there are sufficiently many highly rigid…

We use actions on trees to determine uniform exponential growth for subgroups of $GL_2$.

We give a survey of elliptic hypergeometric functions associated with root systems, comprised of three main parts. The first two form in essence an annotated table of the main evaluation and transformation formulas for elliptic…

It is shown in the framework of the N-component scalar model that the saddle point structure may generate non-trivial renormalization group flow. The spinodal phase separation can be described in this manner and a flat action is found as an…

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 show that the submonoid of all nxn triangular tropical matrices satisfies a nontrivial semigroup identity and provide a generic construction for classes of such identities. The utilization of the Fibonacci number formula gives us an…

We study the globalization problem for a strong partial action $\alpha$ of a monoid $M$ on a semigroup $X$ via the associated rewriting system $(X_M^+,\to)$. We show that the local confluence of $(X_M^+,\to)$ is sufficient for the…

This paper is the first of a sequence of three papers, where the concept of an $\mathbb R$-tree dual to a measured geodesic lamination in a hyperbolic surface is generalized to arbitrary $\mathbb R$-trees provided with a (very small) action…

We propose a relationship between the cohomology of arithmetic groups, and the motivic cohomology of certain (Langlands-)attached motives. The motivic cohomology group in question is that related, by Beilinson's conjecture, to the adjoint…

We provide geometric methods and algorithms to verify, construct and enumerate pairs of words (of specified length over a fixed $m$-letter alphabet) that form identities in the semigroup $\ut{n}$ of $n\times n$ upper triangular tropical…