Related papers: Biautomatic structures in systolic Artin groups
This paper grew out of three tutorial lectures on automatic structures given by the first author at the Logic Colloquium 2007. We discuss variants of automatic structures related to several models of computation: word automata, tree…
We describe the structure of quasiflats in two-dimensio\-nal Artin groups. We rely on the notion of metric systolicity developed in our previous work. Using this weak form of non-positive curvature and analyzing in details the combinatorics…
This is a collection of examples showing how the GAP system can be used to compute information about the generating graphs of finite groups. It includes all examples that were needed for the computational results in the paper "Hamiltonian…
For an arbitrary Euclidean building we define a certain combing, which satisfies the `fellow traveller property' and admits a recursive definition. Using this combing we prove that any group acting freely, cocompactly and by order…
A systolic complex/bridged graph is fit when its (metric) intervals are "not too large". We prove that uniformly locally finite fit systolic complexes have Yu's Property A. In particular, groups acting properly on such complexes have…
We prove that every right-angled Artin group occurs as a finite-index subgroup of the outer automorphism group of another right-angled Artin group. We furthermore show that the latter group can be chosen in such a way that the quotient is…
We characterize groups quasi-isometric to a right-angled Artin group $G$ with finite outer automorphism group. In particular all such groups admit a geometric action on a $CAT(0)$ cube complex that has an equivariant "fibering" over the…
We show that the homology of the automorphism group of a right-angled Artin group stabilizes under taking products with any right-angled Artin group.
We construct a quasi-Garside monoid structure for the free group. This monoid should be thought of as a dual braid monoid for the free group, generalising the constructions by Birman-Ko-Lee and by the author of new Garside monoids for Artin…
We discuss bi-Hamiltonian structures for integrable and superintegrable Hamiltonian system on the list of symplectic four-dimensional real Lie groups are classified by G. Ovando. In addition, we creat corresponding control matrix for…
We show that every right-angled Artin group AG defined by a graph G of finite chromatic number is poly-free with poly-free length bounded between the clique number and the chromatic number of G. Further, a characterization of all…
We introduce the notion of metrically systolic simplicial complexes. We study geometric and large-scale properties of such complexes and of groups acting on them geometrically. We show that all two-dimensional Artin groups act geometrically…
We observe an inductive structure in a large class of Artin groups and exploit this information to deduce the Farrell-Jones isomorphism conjecture for several classes of Artin groups of finite real, complex and affine types.
We prove that shifted cotangent stacks carry a canonical shifted symplectic structure. We also prove that shifted conormal stacks carry a canonical Lagrangian structure. These results were believed to be true but no written proof was…
This paper studies complete rewriting systems and biautomaticity for three interesting classes of finite-rank homogeneous monoids: Chinese monoids, hypoplactic monoids, and sylvester monoids. For Chinese monoids, we first give new…
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.
After reviewing automaton semigroups, we introduce Cayley Automata and the corresponding Cayley Automaton semigroups. We investigate which semigroups are isomorphic to their Cayley Automaton semigroup and give some results for special…
Right-angled Artin groups and their subgroups are of great interest because of their geometric, combinatorial and algorithmic properties. It is convenient to define these groups using finite simplicial graphs. The isomorphism type of the…
We describe the development of the theory of automatic groups. We begin with a historical introduction, define the concepts of automatic, biautomatic and combable groups, derive basic properties, then explain how hyperbolic groups and the…
This is a collection of examples showing how the GAP system can be used to compute information about the probabilistic generation of finite almost simple groups. It includes all examples that were needed for the computational results in the…