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Embeddings of right-angled Artin groups  [PDF]
Travis Scrimshaw
Mathematics , 2010,
Abstract: We explicitly construct an embedding of a right-angled Artin group into a classical pure braid group. Using this we obtain a number of corollaries describing embeddings of arbitrary Artin groups into right-angled Artin groups and linearly independent subgroups of a right-angled Artin group.
Pushing fillings in right-angled Artin groups  [PDF]
Aaron Abrams,Noel Brady,Pallavi Dani,Moon Duchin,Robert Young
Mathematics , 2010, DOI: 10.1112/jlms/jds064
Abstract: We construct "pushing maps" on the cube complexes that model right-angled Artin groups (RAAGs) in order to study filling problems in certain subsets of these cube complexes. We use radial pushing to obtain upper bounds on higher divergence functions, finding that the k-dimensional divergence of a RAAG is bounded by r^{2k+2}. These divergence functions, previously defined for Hadamard manifolds to measure isoperimetric properties "at infinity," are defined here as a family of quasi-isometry invariants of groups; thus, these results give new information about the QI classification of RAAGs. By pushing along the height gradient, we also show that the k-th order Dehn function of a Bestvina-Brady group is bounded by V^{(2k+2)/k}. We construct a class of RAAGs called "orthoplex groups" which show that each of these upper bounds is sharp.
Abelian splittings of Right-Angled Artin Groups  [PDF]
Daniel Groves,Michael Hull
Mathematics , 2015,
Abstract: We characterize when (and how) a Right-Angled Artin group splits nontrivially over an abelian subgroup.
Topology of Random Right Angled Artin Groups  [PDF]
Armindo Costa,Michael Farber
Mathematics , 2009,
Abstract: In this paper we study topological invariants of a class of random groups. Namely, we study right angled Artin groups associated to random graphs and investigate their Betti numbers, cohomological dimension and topological complexity. The latter is a numerical homotopy invariant reflecting complexity of motion planning algorithms in robotics. We show that the topological complexity of a random right angled Artin group assumes, with probability tending to one, at most three values. We use a result of Cohen and Pruidze which expresses the topological complexity of right angled Artin groups in combinatorial terms. Our proof deals with the existence of bi-cliques in random graphs.
On the arboreal structure of right-angled Artin groups  [PDF]
?erban A. Basarab
Mathematics , 2009,
Abstract: The present article continues the study of median groups initiated in [6, 9, 10]. Some classes of median groups are introduced and investigated with a stress upon the class of the so called A-groups which contains as remarkable subclasses the lattice ordered groups and the right-angled Artin groups. Some general results concerning A-groups are applied to a systematic study of the arboreal structure of right-angled Artin groups. Structure theorems for foldings, directions, quasidirections and centralizers are proved.
Homology of subgroups of right-angled Artin groups  [PDF]
Graham Denham
Mathematics , 2006,
Abstract: We describe the (co)homology of a certain family of normal subgroups of right-angled Artin groups that contain the commutator subgroup, as modules over the quotient group. We do so in terms of (skew) commutative algebra of squarefree monomial ideals.
An introduction to right-angled Artin groups  [PDF]
Ruth Charney
Mathematics , 2006,
Abstract: Recently, right-angled Artin groups have attracted much attention in geometric group theory. They have a rich structure of subgroups and nice algorithmic properties, and they give rise to cubical complexes with a variety of applications. This survey article is meant to introduce readers to these groups and to give an overview of the relevant literature.
The strong Atiyah conjecture for right-angled Artin and Coxeter groups  [PDF]
Peter Linnell,Boris Okun,Thomas Schick
Mathematics , 2010, DOI: 10.1007/s10711-011-9631-y
Abstract: We prove the strong Atiyah conjecture for right-angled Artin groups and right-angled Coxeter groups. More generally, we prove it for groups which are certain finite extensions or elementary amenable extensions of such groups.
Divergence in right-angled Coxeter groups  [PDF]
Pallavi Dani,Anne Thomas
Mathematics , 2012,
Abstract: Let W be a 2-dimensional right-angled Coxeter group. We characterise such W with linear and quadratic divergence, and construct right-angled Coxeter groups with divergence polynomial of arbitrary degree. Our proofs use the structure of walls in the Davis complex.
The cohomology of right angled Artin groups with group ring coefficients  [PDF]
Craig Jensen,John Meier
Mathematics , 2004,
Abstract: We give an explicit formula for the cohomology of a right angled Artin group with group ring coefficients in terms of the cohomology of its defining flag complex.
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