Related papers: On groups with finitely many Conradian orderings

We present some Zermelo-Fraenkel consistency results regarding bi-orderability of groups, as well as a construction of groups with Conradian orders whose every action on metric spaces has bounded orbits. A classical consequence of the…

Let G be a group and let O_G denote the set of left orderings on G. Then O_G can be topologized in a natural way, and we shall study this topology to answer three conjectures. In particular we shall show that O_G can never be countably…

We construct total orders on the vertex set of an oriented tree. The orders are based only on up-down counts at the interior vertices and the edges along the unique geodesic from a given vertex to another. As an application, we provide a…

We construct a finitely presented (two-sided) totally orderable group with insoluble word problem.

We arrange classical small cancellation constructions to produce left-orderable groups: we show that every finitely generated group is the quotient of a left-ordered small cancellation group by a finitely generated kernel (Rips…

In this paper we present the following two results: we give an explicit description of the space of orderings of the field Q(x) as an inverse limit of finite spaces of orderings and we provide a new, simple proof of the fact that the class…

We are concerned with orderable groups and particularly those with orderings invariant not only under multiplication, but also under a given automorphism or family of automorphisms. Several applications to topology are given: we prove that…

Let $G$ be a group. We can topologize the spaces of left-orderings $LO(G)$ and bi-orderings $O(G)$ of $G$ with the product topology. These spaces may or may not have isolated points. It is known that $LO(F_2)$ has no isolated points, where…

The goal of this paper is to show the following result: For every integer $n\geq 2$ there is a countable orderable group such that its space of orders is countable and has Cantor-Bendixson rank $n$. We show this by explicitly constructing a…

A well ordering < of a topological space X is "left-separating" if $\{x'\in X: x'< x\}$ is closed in X for any x in X. A space is "left-separated" if it has a left-separating well-ordering. The left-separating type, $ord_l(X)$, of a…

Motivated by recent activity in low-dimensional topology, we provide a new criterion for left-orderability of a group under the assumption that the group is circularly-orderable: A group $G$ is left-orderable if and only if $G \times…

In this paper, we introduce the notion of circular orderability for quandles. We show that the set all right (respectively left) circular orderings of a quandle is a compact topological space. We also show that the space of right…

It is well-known that the direct product of left-orderable groups is left-orderable and that, under a certain condition, the semi-direct product of left-orderable groups is left-orderable. We extend this result and show that, under a…

We describe a simple scheme for constructing finitely generated monoids in which left-divisibility is a linear ordering and for practically investigating these monoids. The approach is based on subword reversing, a general method of…

We provide an infinite family of left-ordered groups, all of which have a positive cone that is finitely generated as a semigroup. This family includes the Klein bottle group and the braid group B_3.

We consider group orders and right-orders which are discrete, meaning there is a least element which is greater than the identity. We note that free groups cannot be given discrete orders, although they do have right-orders which are…

We construct the first examples of finitely presented simple groups of orientation-preserving homeomorphisms of the real line. Our examples are also of type $F_{\infty}$, have infinite geometric dimension, and admit a nontrivial homogeneous…

We give sufficient conditions for left- and bi-orderability of fundamental groups of Ore categories in terms of indirect factors, including Thompson groups and many of their generalizations. Besides recovering known results, we prove that…

We discuss actions of free groups on the circle with "ping-pong" dynamics; these are dynamics determined by a finite amount of combinatorial data, analogous to Schottky domains or Markov partitions. Using this, we show that the free group…

The space $\mathcal{Z}$ of leftinvariant orthogonal almost complex structures, keeping the orientation, on 6-dimensional Lie groups is researched. To get explicit view of this space elements the isomorphism of $\mathcal{Z}$ and…