Related papers: On lengths on semisimple groups

In this work, we study good semigroups of $\mathbb{N}^n$ introducing the definition of length and genus for these objects. We show how to count the local good semigroup with a fixed genus. Furthermore, we study the relationships of these…

We prove that every transitive and non minimal semigroup with dense minimal points is sensitive. When the system is almost open, we obtain a generalization of this result.

A group is boundedly simple if, for some constant N, every nontrivial conjugacy class generates the whole group in N steps. For a large class of trees, Tits proved simplicity of a canonical subgroup of the automorphism group, which is…

We provide a simple proof of the Holonomy Theorem using a new Lyndon-Chiswell length function on the Karnofsky-Rhodes expansion of a semigroup. Unexpectedly, we have both a left and a right action on the Chiswell tree by elliptic maps.

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…

The aim of this note is to give a geometric proof for classical local rigidity of lattices in semisimple Lie groups. We are reproving well known results in a more geometric (and hopefully clearer) way.

In this paper we prove a theorem describing the local topology of the boundary of a hyperbolic group in terms of its global topology: the boundary is locally simply connected if and only if the complement of any point in the boundary is…

We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor bonding map is either an epimorphism with finite kernel or the projection from a product by a…

We show that, in compact semisimple Lie groups and Lie algebras, any neighbourhood of the identity gets mapped, under the commutator map, to a neighbourhood of the identity.

We prove that on a metrizable, compact, zero-dimensional space every free action of an amenable group is measurably isomorphic to a minimal $G$-action with the same, i.e. affinely homeomorphic, simplex of measures.

We complete the quasi-isometric classification of irreducible lattices in semisimple Lie groups over nondiscrete locally compact fields of characteristic zero by showing that any quasi-isometry of a rank one S-arithmetic lattice in a…

We study the collection of group structures that can be realized as a group of rational points on an elliptic curve over a finite field (such groups are well known to be of rank at most two). We also study various subsets of this collection…

We prove that infinite definably simple locally finite groups of finite centraliser dimension are simple groups of Lie type over locally finite fields. Then, we identify conditions on automorphisms of a stable group that make it resemble…

We demonstrate that And\'ujar Guerrero, Thomas and Walsberg's results on definable compactness in o-minimal structures still hold true in definably complete locally o-minimal structures. As an application, we show that a definably simple…

We show that many important varieties and sets of varieties of semigroups may be defined by relatively simple and transparent first-order formulas in the lattice of all semigroup varieties.

Let G be a locally compact Hausdorff group in which every element is of finite order, and let P(G) denote the class of all regular probability measures on G. In this note, it is observed that a characterization of algebraically regular…

Commability is the finest equivalence relation between locally compact groups such that $G$ and $H$ are equivalent whenever there is a continuous proper homomorphism $G \to H$ with cocompact image. Answering a question of Cornulier, we show…

This paper presents a proof of the existence of standard symplectic coordinates near a set of smooth, orthogonally intersecting symplectic submanifolds. It is a generalization of the standard symplectic neighborhood theorem. Moreover, in…

A group is SimpHAtic if it acts geometrically on a simply connected simplicially hereditarily aspherical (SimpHAtic) complex. We show that finitely presented normal subgroups of the SimpHAtic groups are either: finite, or of finite index,…

Let (M, g) be a compact Einstein manifold with non-empty boundary. We prove that Killing fields at the boundary extend to Killing fields of any (M, g) provided the boundary is weakly convex and a simple condition on the fundamental group…