Related papers: Condensation and left-orderable groups

Let $\F$ be an algebraically closed field. Let $\V$ be a vector space equipped with a non-degenerate symmetric or symplectic bilinear form $B$ over $\F$. Suppose the characteristic of $\F$ is \emph{large}, i.e. either zero or greater than…

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 provide the combinatorial proofs of the log-convexity for the derangement numbers in the symmetric group $\mathfrak{S}_n$, hyperoctahedral group $\mathfrak{B}_n$, and the demihyperoctahedral group $\mathfrak{D}_n$. We also show that the…

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…

For a group $ G $ we consider its tensor square $G \otimes G$ and exterior square $G \wedge G$. We prove that for a circularly orderable group $G$, under some assumptions on $H_1(G)$ and $H_2(G)$, its exterior square and tensor square are…

We characterize conjugacy classes of isometries of odd prime order in unimodular Z-lattices. This is applied to give a complete classification of odd prime order non-symplectic automorphisms of irreducible holomorphic symplectic manifolds…

We study the topological space of left-orderings of the braid group, and its subspace of Nielsen-Thurston orderings. Our main result is that no Nielsen-Thurston ordering is isolated in the space of braid orderings. In the course of the…

This paper gives a new way of characterizing L-space $3$-manifolds by using orderability of quandles. Hence, this answers a question of Adam Clay et al. [Question 1.1 of Canad. Math. Bull. 59 (2016), no. 3, 472-482]. We also investigate…

We motivate and study the class $\mathcal{C}$ of countable groups $G$ such that the conjugacy relation between minimal actions of $G$ on $\mathbb{R}$ by orientation-preserving homeomorphisms is smooth -- that is, admits a Borel transversal.…

We introduce a refinement of bounded cohomology and prove that the suitable comparison homomorphisms vanish for an amenable group. We investigate in this context Thompson's group F and provide further evidence towards its amenability. We…

In this survey, we discuss a series of linearization problems--for Poisson structures, Lie algebroids, and Lie groupoids. The last problem involves a conjecture on the structure of proper groupoids. Attempting to prove this by the method of…

Smectic materials represent a unique state between fluids and solids, characterized by orientational and partial positional order, making them notoriously difficult to model, particularly in confining geometries. We propose a complex order…

We are interested in the classification of left-invariant symplectic structures on Lie groups. Some classifications are known, especially in low dimensions. In this paper we establish a new approach to classify (up to automorphism and…

We introduce a Dehornoy-like ordering of groups, which is a generalization of the Dehornoy ordering of the braid groups. Under a weak assumption which we call Property F, we show that Dehornoy-like orderings have properties similar to the…

In this article, we focus on the left (translation) actions on noncommutative compact connected Lie groups ${\rm SU}(2) \times T^n$. We define the rotation vectors of the left actions induced by the elements in the maximal tori of ${\rm…

The Baumslag-Solitar groups: BS(m,n)=<x,y| x y^{m} x^{-1} = y^{n}> are some of the simplest interesting infinite groups which are not lattices in Lie groups. They have been studied in depth from the point of view of combinatorial group…

We establish connections between contact isometry groups of certain contact manifolds and compactly supported symplectomorphism groups of their symplectizations. We apply these results to investigate the space of symplectic embeddings of…

A characterization is given of the subsets of a group that extend to the positive cone of a right order on the group and used to relate validity of equations in lattice-ordered groups (l-groups) to subsets of free groups that extend to…

This expository paper explores the interaction of group ordering with topological questions, especially in dimensions 2 and 3. Among the topics considered are surfaces, braid groups, 3-manifolds and their structures such as foliations and…

Condensed mathematics, developed by Clausen and Scholze over the last few years, is a new way of studying the interplay between algebra and geometry. It replaces the concept of a topological space by a more sophisticated but better-behaved…