Related papers: The minimal genus problem for right angled Artin g…

Consider the mapping class group $\Mod_{g,p}$ of a surface $\Sigma_{g,p}$ of genus $g$ with $p$ punctures, and a finite collection $\{f_1,...,f_k\}$ of mapping classes, each of which is either a Dehn twist about a simple closed curve or a…

Determining the minimum genus of a graph is a fundamental optimisation problem in the study of network design and implementation as it gives a measure of non-planarity of graphs. In this paper, we are concerned with determining the smallest…

For the right-angled Artin group action on the extension graph, it is known that the minimal asymptotic translation length is bounded above by 2 provided that the defining graph has diameter at least 3. In this paper, we show that the same…

In this paper we give an algorithm for computing the conjugacy growth series for a right-angled Artin group, based on a natural language of minimal length conjugacy representatives. In addition, we provide a further language of unique…

We show that the fundamental groups of any two closed irreducible non-geometric graph-manifolds are quasi-isometric. This answers a question of Kapovich and Leeb. We also classify the quasi-isometry types of fundamental groups of…

An even Artin group is a group which has a presentation with relations of the form $(st)^n=(ts)^n$ with $n\ge 1$. With a group $G$ we associate a Lie $\mathbb Z$-algebra $\mathcal{TG}r(G)$. This is the usual Lie algebra defined from the…

We show that the outer automorphism groups of graph products of finitely generated abelian groups satisfy the Tits alternative, are residually finite, their so-called Torelli subgroups are finitely generated, and they satisfy a dichotomy…

A topological group is minimal if it does not admit a strictly coarser Hausdorff group topology. We provide a sufficient and necessary condition for the minimality of the semidirect product $G\leftthreetimes P,$ where $G$ is a compact…

Let $\Gamma$ be a finite graph and let $A(\Gamma)$ be the corresponding right-angled Artin group. From an arbitrary basis $\mathcal B$ of $H^1(A(\Gamma),\mathbb F)$ over an arbitrary field, we construct a natural graph $\Gamma_{\mathcal B}$…

This chapter provides a comprehensive survey of foundational results and recent advances concerning minimal generating sets for the mapping class group of a nonorientable surface, $\mathrm{Mod}(N_{g})$, and its index-two twist subgroup,…

We describe sufficient conditions which guarantee that a finite set of mapping classes generate a right-angled Artin group quasi-isometrically embedded in the mapping class group. Moreover, under these conditions, the orbit map to…

In this paper we solve the conjugacy problem for several classes of virtual right-angled Artin groups, using algebraic and geometric techniques. We show that virtual RAAGs of the form $A_{\phi} = A_{\Gamma} \rtimes_{\phi}…

We prove that second rational homology of the Torelli group of an orientable closed surface of genus g is finite dimensional for g at least 51. This rules out the simplest obstruction to the Torelli group being finitely presented and…

We study a variety of natural constructions from topological combinatorics, including matching complexes as well as other graph complexes, from the perspective of the graph minor category of \parencite{MiProRa}. We prove that these…

In this article we prove the topological minimality of unions of several almost orthogonal planes of arbitrary dimensions. A particular case was proved in arXiv:1103.1468, where we proved the Almgren minimality (which is a weaker property…

The Tits Conjecture, proved by Crisp and Paris, states that squares of the standard generators of any Artin group generate an obvious right-angled Artin subgroup. We consider a larger set of elements consisting of all the centers of the…

We study the class N of graphs, the right-angled Artin groups defined on which do not contain surface subgroups. We prove that a presumably smaller class N' is closed under amalgamating along complete subgraphs, and also under adding…

It has long been known that the combinatorial properties of a graph $\Gamma$ are closely related to the group theoretic properties of its right angled artin group (raag). It's natural to ask if the graph homomorphisms are similarly related…

A drawing of a graph on a surface is independently even if every pair of nonadjacent edges in the drawing crosses an even number of times. The $\mathbb{Z}_2$-genus of a graph $G$ is the minimum $g$ such that $G$ has an independently even…

We discuss various types of Tits Alternative for subgroups of graph products of groups, and prove that, under some natural conditions, a graph product of groups satisfies a given form of Tits Alternative if and only if each vertex group…