Related papers: Condensation and left-orderable groups

The arguments of Cannon, Floyd, Grayson and Thurston showing that solve geometry groups are not almost convex also show that solvable Baumslag-Solitar groups are not almost convex.

We consider the torsion of homology groups of right pointed sets over a partially commutative monoid M(E,I)

We introduce right amenability, right F{\o}lner nets, and right paradoxical decompositions for left homogeneous spaces and prove the Tarski-F{\o}lner theorem for left homogeneous spaces with finite stabilisers. It states that right…

In this paper we study the complex symmetry in the several variable Fock space by using the techniques of weighted composition operators and semigroups. We characterize unbounded weighted composition operators that are (real) complex…

We investigate the rank gradient and growth of torsion in homology in residually finite groups. As a tool, we introduce a new complexity notion for generating sets, using measured groupoids and combinatorial cost. As an application we prove…

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…

Many non-locally compact second countable groups admit a comeagre conjugacy class. For example, this is the case for the automorphism group of the rational order and the automorphism group of the random graph [Truss]. A. Kechris and C.…

We prove that one-relator groups with negative immersions are hyperbolic and virtually special; this resolves a recent conjecture of Louder and Wilton. As a consequence, one-relator groups with negative immersions are residually finite,…

We give the first examples of groups which admit a tame combing with linear radial tameness function with respect to any choice of finite presentation, but which are not minimally almost convex on a standard generating set. Namely, we…

We give a unified solution to the conjugacy problem for Thompson's groups F, T, and V. The solution uses strand diagrams, which are similar in spirit to braids and generalize tree-pair diagrams for elements of Thompson's groups. Strand…

We study the structure of generalized Baumslag-Solitar groups from the point of view of their (usually non-unique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of…

In this work we exhibit flexibility phenomena for some (countable) groups acting by order preserving homeomorphisms of the line. More precisely, we show that if a left orderable group admits an amalgam decomposition of the form…

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…

Lie symmetry group method is applied to study for the higher order Camassa-Holm equation. The symmetry group and its optimal system are given. Furthermore, preliminary classification of its group invariant solutions, symmetry reduction and…

We prove a few basic facts about the space of bi-invariant (or left-invariant) total order relations on a torsion-free, nonabelian, nilpotent group G. For instance, we show that the space of bi-invariant orders has no isolated points (so it…

There has been interest recently concerning when a left ordered group is locally indicable. Bergman and Tararin have shown that not all left ordered groups are locally indicable, but all known examples contain a nonabelian free subgroup. We…

The conjugacy problem belongs to algorithmic group theory. It is the following question: given two words x, y over generators of a fixed group G, decide whether x and y are conjugated, i.e., whether there exists some z such that zxz^{-1} =…

This is an almost self-contained monograph (containing some new results) on left-orderable groups which mostly rely on dynamical and probabilistic aspects, but also on geometric, combinatorial, analytic, and topological ones. This new…

This is a draft of a book submitted for publication by the AMS. Its theme is the remarkable interplay, accelerating in the last few decades, between topology and the theory of orderable groups, with applications in both directions. It…

This paper pursues an investigation on groups equipped with an $L$-ordered relation, where $L$ is a fixed complete complete Heyting algebra. First, by the concept of join and meet on an $L$-ordered set, the notion of an $L$-lattice is…